Complete set of deuteron analyzing powers from (d)over-right-arrowp elastic scattering at 190 MeV/nucleon
K. Sekiguchi, H. Witała, T. Akieda, D. Eto, H. Kon, Y. Wada, A. Watanabe, S. Chebotaryov, M. Dozono, J. Golak, H. Kamada, S. Kawakami, Y. Kubota, Y. Maeda, K. Miki, E. Milman, A. Ohkura, H. Sakai, S. Sakaguchi, N. Sakamoto, M. Sasano, Y. Shindo, R. Skibiński, H. Suzuki, M. Tabata, T. Uesaka, T. Wakasa, K. Yako, T. Yamamoto, Y. Yanagisawa, J. Yasuda
abstract
All deuteron analyzing powers for elastic deuteron-proton (dp) scattering have been measured with a polarized deuteron beam at 186.6 MeV/nucleon. They are compared with results of three-nucleon Faddeev calculations based on the standard, high-precision nucleon-nucleon (NN) potentials alone or combined with commonly used three-nucleon force (3NF) models such as the Tucson-Melbourne ' 99 or the Urbana IX. Predicted 3NF effects localized at backward angles are supported only partially by the data. The data are also compared to predictions based on locally regularized chiral NN potentials. An estimation of theoretical truncation uncertainties in the consecutive orders of chiral expansion suggests that the observed discrepancies between this modern theory and the data could probably be explained by including chiral 3NF's in future calculations. A systematic comparison to the deuteron analyzing power data previously taken at incident energies from 70 to 294 MeV/nucleon clearly shows that not only the cross section but also the analyzing powers reveal growing 3NF effects when the three-nucleon system energy is increased.
ELASTIC NUCLEON-DEUTERON SCATTERING WITH THE NUCLEON-NUCLEON OPE-GAUSSIAN FORCE AT E=65 MeV - INTRODUCTORY STUDIES
Y. Volkotrub, R. Skibiński, J. Golak, K. Topolnicki, H. Witała
abstract
We study the elastic nucleon-deuteron (Nd) scattering process at the incoming nucleon laboratory energy E = 6 5 MeV working within the formalism of Faddeev equations. We employ, for the first time in the elastic Nd scattering, the OPE-Gaussian nucleon-nucleon (NN) potential and confirm its high quality by comparing our predictions for the differential cross section with results based on the AV18 potential as well as with available data. We also estimate the theoretical uncertainty of this observable originating from uncertainties of the OPE-Gaussian model parameters. We find the relative uncertainties to be smaller than 0.8% for the differential cross section. The correlations between various parameters of the OPE-Gaussian are also shown.
Operator form of the three-nucleon scattering amplitude
K. Topolnicki, J. Golak, R. Skibiński, H. Witała
abstract
To extend the applications of the so-called "three-dimensional" formalism to the description of three-nucleon scattering within the Faddeev formalism, we develop a general form of the three-nucleon scattering amplitude. This form significantly decreases the numerical complexity of the "three-dimensional" calculations by reducing the scattering amplitude to a linear combination of momentum-dependent spin operators and scalar functions of momenta. The number and structure of the spin operators is fixed and the scalar functions can be represented numerically using standard methods such as multidimensional arrays. In this paper, we show that all orders of the iterated Faddeev equation can be written in this general form. We argue that calculations utilizing the three-nucleon force will also conform to the same general form. Additionally, we show how the general form of the scattering amplitude can be used to transform the Faddeev equation to make it suitable for numerical calculations using iterative methods.
Modern Chiral Forces Applied to the Nucleon-Deuteron Radiative Capture
R. Skibiński, J. Golak, K. Topolnicki, H. Witała, E. Epelbaum, H. Kamada, H. Krebs, UG. Meissner, A. Nogga
abstract
The chiral nucleon-nucleon interaction with semi-local regularization up to the fifth order of chiral expansion is applied to the nucleon-deuteron radiative capture process. Our theoretical approach is based on the formalism of Faddeev equations and the Siegert theorem is exploited to construct the electromagnetic current operator. The very weak dependence of the differential cross section on values of the regularization parameter is observed. This suggests that the improved chiral two-body interaction is a promising starting point to study electromagnetic processes at low energies.
Three Nucleon Scattering in a 3D Approach at the First Order
K. Topolnicki, J. Golak, R. Skibiński, H. Witała
abstract
The "three dimensional" (3D) approach to few-nucleon calculations, instead of working with partial wave states, uses the momentum degrees of freedom of the nucleons directly. As a result, 3D calculations are equivalent to incorporating all partial waves into the calculation. This equivalence is limited by the available computational resources, nonetheless, the new approach provides an opportunity to construct numerical descriptions of physical systems that were previously unavailable with more traditional methods. We present selected observables for the neutron-deuteron inelastic scattering process calculated using the 3D approach and the traditional partial wave approach. This comparison was carried out using the first order terms of the series expansion of the Faddeev equations and is a strong motivator for a development of a complete 3D calculation that utilizes all orders.
Muon Capture on H-3
J. Golak, R. Skibiński, H. Witała, K. Topolnicki, H. Kamada, A. Nogga, LE. Marcucci
abstract
The mu(-) + (3) H -> nu(mu) + n + n + n capture reaction is studied under full inclusion of final-state interactions with the AV18 nucleon-nucleon potential and the Urbana IX three-nucleon force. We employ the single nucleon weak current operator comprising the dominant relativistic corrections to obtain first estimates of the total capture rates based on realistic forces. Our results are compared with older theoretical predictions.
Role of the Total Isospin 3/2 Component in Three-Nucleon Reactions
H. Witała, J. Golak, R. Skibiński, K. Topolnicki, E. Epelbaum, K. Hebeler, H. Kamada, H. Krebs, UG. Meissner, A. Nogga
abstract
We discuss the role of the three-nucleon isospin amplitude in elastic neutron-deuteron scattering and in the deuteron breakup reaction. The contribution of this amplitude originates from charge-independence breaking of the nucleon-nucleon potential and is driven by the difference between neutron-neutron (proton-proton) and neutron-proton forces. We study the magnitude of that contribution to the elastic scattering and breakup observables, taking the locally regularized chiral NLO nucleon-nucleon potential supplemented by the chiral NLO three-nucleon force. For comparison we employ also the Av18 nucleon-nucleon potential combined with the Urbana IX three-nucleon force. We find that the isospin component is important for the breakup reaction and the proper treatment of charge-independence breaking in this case requires the inclusion of the state with isospin . For neutron-deuteron elastic scattering the contributions are insignificant and charge-independence breaking can be accounted for by using the effective t-matrix generated with the so-called rule.
Muon capture on H-3
J. Golak, R. Skibiński, H. Witała, K. Topolnicki, H. Kamada, A. Nogga, LE. Marcucci
abstract
The mu(-) + H-3 ->nu(mu) + n + n + n capture reaction is studied under full inclusion of final-state interactions. Predictions for the three-body breakup of H-3 are calculated with the AV18 potential, augmented by the Urbana IX three-nucleon force. Our results are based on the single-nucleon weak-current operator comprising the dominant relativistic corrections. This work is a natural extension of our investigations of the mu(-) + He-3 -> nu(mu)+ H-3, mu(-) + He-3 -> nu(mu)+ n + d and mu(-) + He-3 -> nu(mu) + n + n + p capture reactions presented in Golak et al.
The general operator form for the total-momentum-dependent nucleon-nucleon potential
K. Topolnicki, J. Golak, R. Skibiński, H. Witała
abstract
In this paper we describe a procedure to obtain the general operator form of two-nucleon (2N) potentials and apply it to the case of the 2N potential that has an additional dependence on the total momentum of the system. This violates Galilean invariance but terms including the total momentum appear in some relativistic approaches. In operator form, the potential is expressed as a linear combination of a fixed number of known spin-momentum operators and scalar functions of momenta. Since the scalar functions effectively define the potentials, using the operator form significantly reduces the number of parameters that are needed in numerical implementations. The proposed operator form explicitly obeys the usual symmetries of rotational invariance, particle exchange, time reflection and parity.
Testing semilocal chiral two-nucleon interaction in selected electroweak processes
R. Skibiński, J. Golak, K. Topolnicki, H. Witała, E. Epelbaum, H. Krebs, H. Kamada, UG. Meissner, A. Nogga
abstract
The recently developed semilocal improved chiral nucleon-nucleon interaction is used for the first time to study several electromagnetic and weak processes at energies below the pion production threshold. Cross sections and selected polarization observables for deuteron photodisintegration, nucleon-deuteron radiative capture, three-body He-3 photodisintegration, as well as capture rates for decays of the muonic H-2 and He-3 atoms are calculated. The Lippmann-Schwinger and Faddeev equations in momentum space are solved to obtain nuclear states. The electromagnetic current operator is taken as a single nucleon current supplemented by many-body contributions induced via the Siegert theorem. For muon capture processes the nonrelativistic weak current together with the dominant relativistic corrections is used. Our results compare well with experimental data, demonstrating the same quality as is observed for the semiphenomenological Argonne V18 potential. Compared to the older version of the chiral potential with a nonlocal regularization, a much smaller cut-off dependence is found for the state-of-art chiral local interaction employed in this paper. Finally, estimates of errors due to the truncation of the chiral expansion are given.
Few-nucleon systems with state-of-the-art chiral nucleon-nucleon forces
S. Binder, A. Calci, E. Epelbaum, RJ. Furnstahl, J. Golak, K. Hebeler, H. Kamada, H. Krebs, J. Langhammer, S. Liebig, P. Maris, UG. Meissner, D. Minossi, A. Nogga, H. Potter, R. Roth, R. Skibiński, K. Topolnicki, JP. Vary, H. Witała
abstract
We apply improved nucleon-nucleon potentials up to fifth order in chiral effective field theory, along with a new analysis of the theoretical truncation errors to study nucleon-deuteron (Nd) scattering and selected low-energy observables in H-3, He-4, and Li-6. Calculations beyond second order differ from experiment well outside the range of quantified uncertainties, providing truly unambiguous evidence for missing three-nucleon forces within the employed framework. The sizes of the required three-nucleon-force contributions agree well with expectations based on Weinberg's power counting. We identify the energy range in elastic Nd scattering best suited to study three-nucleon-force effects and estimate the achievable accuracy of theoretical predictions for various observables.
Orthogonal polynomial approach to calculate the two-nucleon transition operator in three dimensions
K. Topolnicki, J. Golak, R. Skibiński, H. Witała
abstract
We give a short report on the possibility to use orthogonal polynomials (OP) in calculations that involve the two-nucleon (2N) transition operator. The presented work adds another approach to the set of previously developed methods (described in Phys. Rev. C 81, 034006 (2010); Few-Body Syst. 53, 237 (2012); K. Topolnicki, PhD thesis, Jagiellonian University (2014)) and is applied to the transition operator calculated at laboratory kinetic energy 300MeV. The new results for neutron-neutron and neutron-proton scattering observables converge to the results presented in Few-Body Syst. 53, 237 (2012) and to results obtained using the Arnoldi algorithm (Y. Saad, Iterative methods for sparse linear systems (SIAM Philadelphia, PA, USA 2003)). The numerical cost of the calculations performed using the new scheme is large and the new method can serve only as a backup to cross-check the previously used calculation schemes.
Studies of three-nucleon systems with improved chiral forces
R. Skibiński, J. Golak, K. Topolnicki, H. Witała, E. Epelbaum
abstract
Recently developed chiral two-nucleon (2N) potentials are applied to various processes in three-nucleon (3N) systems within the approach based on Faddeev equations. The predictions for the cross sections in elastic nucleon-deuteron (Nd) scattering and for radiative proton-deuteron (pd) capture are similar to results based on the AV] 8 potential. The very good convergence with respect to the chiral expansion and a weak dependence on a regularization parameter are observed. This gives hope that the Hamiltonian combining these 2N potentials with consistent 3N forces will become an important tool to study nuclear structure and processes.
Elastic nucleon-deuteron scattering and breakup with chiral forces
H. Witała, J. Golak, R. Skibiński, K. Topolnicki
abstract
Results on three-nucleon (3N) elastic scattering and breakup below the pion production threshold are discussed. The large discrepancies found between a theory based on numerical solutions of 3N Faddeev equations with standard nucleon-nucleon (NN) potentials only and data point to the need for three-nucleon forces (3NF's). This notion is supported by the fact that another possible reason for the discrepancies in elastic nucleon-deuteron (Nd) scattering, relativistic effects, turned out to be small. Results for a new generation of chiral NN forces (up to (NLO)-L-4) together with theoretical truncation errors are shown. They support conclusions obtained with standard NN potentials
Break-up channels in muon capture on He-3
J. Golak, R. Skibiński, H. Witała, K. Topolnicki, AE. Elmeshneb, H. Kamada, A. Nogga, LE. Marcucci
abstract
The mu(-) + He-3 -> nu(mu) + n + d and mu(-) + He-3 -> nu(mu) + n + n + p capture reactions are studied under full inclusion of final state interactions with the AV18 nucleon-nucleon potential, augmented by the Urbana IX three-nucleon force, and employing the single nucleon weak current operator. We give first realistic estimates of the total capture rates: 544 s(-1) and 154 s(-1) for the n + d and n + n + p channels, respectively. Our results are compared with the most recent experimental data, finding a rough agreement for the total capture rates, but failing to reproduce the differential capture rates.
Properties of He-4 and Li-6 with improved chiral EFT interactions
P. Maris, S. Binder, A. Calci, E. Epelbaum, RJ. Furnstahl, J. Golak, K. Hebeler, H. Kamada, H. Krebs, J. Langhammer, S. Liebig, UG. Meissner, D. Minossi, A. Nogga, H. Potter, R. Roth, R. Skibiński, K. Topolnicki, JP. Vary, H. Witała
abstract
We present recent results for He-4 and Li-6 obtained with improved NN interactions derived from chiral effective field theory up to (NLO)-L-4. The many-body calculations are performed order-by-order in the chiral expansion. At (NLO)-L-3 and (NLO)-L-4 additional renormalization using the Similarity Renormalization Group is adopted to improve numerical convergence of the many-body calculations. We discuss results for the ground state energies, as well as the magnetic moment and the low-lying spectrum of Li-6.
(NLO)-L-3 Chiral Predictions for Spin Observables in Nucleon-Deuteron Elastic Scattering at Low Energies
R. Skibiński, J. Golak, K. Topolnicki, H. Witała
abstract
The chiral next-to-next-to-next-to leading order nuclear forces(1-3) are used to obtain predictions for spin observables in elastic nucleon-deuteron scattering at E = 13 MeV. The three-nucleon force is taken into account with all its complexity, including the short-range part and relativistic corrections. Presented examples of the polarization observables for elastic nucleon-deuteron scattering show visible contributions from these new structures in the three-nucleon potential which emerge for the first time at the next-to-next-to-next-to leading order. However, our results suggest that some modifications of the currently used model of the nuclear forces are necessary.
Measurement of the doubly-polarized He-3((gamma)over-right-arrow, n)pp reaction at 16.5 MeV and its implications for the GDH sum rule
G. Laskaris, X. Yan, JM. Mueller, WR. Zimmerman, W. Xiong, MW. Ahmed, T. Averett, PH. Chu, A. Deltuva, C. Flower, AC. Fonseca, H. Gao, J. Golak, JN. Heideman, HJ. Karwowski, M. Meziane, PU. Sauer, R. Skibiński, II. Strakovsky, HR. Weller, H. Witała, YK. Wu
abstract
We report new measurements of the double-polarized photodisintegration of He-3 at an incident photon energy of 16.5 MeV, carried out at the High Intensity gamma-ray Source (HI gamma S) facility located at Triangle Universities Nuclear Laboratory (TUNL). The spin-dependent double-differential cross sections and the contribution from the three-body channel to the Gerasimov-Drell-Hearn (GDH) integrand were extracted and compared with the state-of-the-art three-body calculations. The calculations, which include the Coulomb interaction and are in good agreement with the results of previous measurements at 12.8 and 14.7 MeV, deviate from the new cross section results at 16.5 MeV. The GDH integrand was found to be about one standard deviation larger than the maximum value predicted by the theories. (C) 2015 The Authors. Published by Elsevier B.V.
The Two-Nucleon and Three-Nucleon System in Three Dimensions
K. Topolnicki, J. Golak, H. Witała, R. Skibiński, AE. Elmeshneb
abstract
We present a brief overview of the three-dimensional formalism that is under development in our group. Using the 3D momentum eigenstates of the nucleon directly, instead of relying on the partial wave decomposition of operators involved in the calculations, allows us to use a very direct approach. This in turn enabled us to successfully tackle a large variety of few-body problems. Our calculation of the two nucleon transition operator and bound state can incorporate a very general form of the two-nucleon potential. Calculations of the three-nucleon bound state can include in addition to the two-nucleon potential also a very general operator form of the three-nucleon force. Recently the 3D formalism is also applied to processes that involve electro-weak probes. Carrying out these calculations for a wide spectrum of two-nucleon and three-nucleon potentials using the classical partial wave approach is unpractical due to the complicated spin structure of the operators. Using the 3D formalism, the calculations can be quickly adapted to test new models.
THE CHIRAL LONG-RANGE TWO-PION EXCHANGE ELECTROMAGNETIC CURRENTS IN RADIATIVE NUCLEON-DEUTERON CAPTURE
R. Skibiński, J. Golak, D. Rozpedzik, K. Topolnicki, H. Witała
abstract
The nucleon-deuteron radiative capture process is investigated using the chiral nuclear potentials and the electromagnetic currents developed by the Bochum-Bonn group. While the strong interaction is taken up to the next-to-next-to-leading order, the electromagnetic current consists of a single nucleon current, the leading one-pion exchange one and is supplemented by contributions from the long-range two-pion exchange current at next-to-leading-order. The theoretical predictions for the cross sections as well as analyzing powers show strong dependence on the values of regularization parameters. Only small effects of the three-nucleon force and the long-range two-pion exchange current are observed. The dependence on the choice of regularization parameters results in a big theoretical uncertainty and clearly points to the necessity to include corrections from higher orders of the chiral expansion both for the nuclear forces and currents.
Ab Initio Calculations Of Three-Nucleon Scattering
H. Witała, J. Golak, R. Skibiński, K. Topolnicki
abstract
Results on three-nucleon (3N) elastic scattering below the pion production threshold are discussed with an emphasis on the need for a three-nucleon force (3NF). The large discrepancies found between a theory based on numerical solutions of 3N Faddeev equations with (semi) phenomenological NN potentials only and data point to the need for 3NF's. This notion is supported by the fact that another possible reason for the discrepancies in elastic nucleon-deuteron (Nd) scattering, relativistic effects, turned out to be small. Results for new generation of chiral NN forces (up to (NLO)-L-4) together with theoretical truncation errors are shown.
Low-energy neutron-deuteron reactions with (NLO)-L-3 chiral forces
J. Golak, R. Skibiński, K. Topolnicki, H. Witała, E. Epelbaum, H. Krebs, H. Kamada, UG. Meissner, V. Bernard, P. Maris, J. Vary, S. Binder, A. Calci, K. Hebeler, J. Langhammer, R. Roth, A. Nogga, S. Liebig, D. Minossi
abstract
We solve three-nucleon Faddeev equations with nucleon-nucleon and three-nucleon forces derived consistently in the framework of chiral perturbation theory at next-to-next-to-next-to-leading order in the chiral expansion. In this first investigation we include only matrix elements of the three-nucleon force for partial waves with the total two-nucleon (three-nucleon) angular momenta up to 3 (5/2). Low-energy neutron-deuteron elastic scattering and deuteron breakup reaction are studied. Emphasis is put on Ay puzzle in elastic scattering and cross sections in symmetric-space-star and neutron-neutron quasi-free-scattering breakup configurations, for which large discrepancies between data and theory have been reported.
Calculations of three-nucleon reactions with (NLO)-L-3 chiral forces: achievements and challenges
H. Witała, J. Golak, R. Skibiński, K. Topolnicki
abstract
We discuss the application of the chiral (NLO)-L-3 forces to three-nucleon reactions and point to the challenges which will have to be addressed. Present approaches to solve three-nucleon Faddeev equations are based on a partial-wave decomposition. A rapid increase of the number of terms contributing to the chiral three-nucleon force when increasing the order of the chiral expansion from (NLO)-L-2 to (NLO)-L-3 forced us to develop a fast and effective method of automatized partial-wave decomposition. At low energies of the incoming nucleon below approximate to 20 MeV, where only a limited number of partial waves is required, this method allowed us to perform calculations of reactions in the three-nucleon continuum using (NLO)-L-3 two- and three-nucleon forces. It turns out that inclusion of consistent chiral interactions, with relativistic 1/m corrections and short-range 2 pi-contact term omitted in the (NLO)-L-3 three-nucleon force, does not explain the long standing low energy A(y)-puzzle. We discuss problems arising when chiral forces are applied at higher energies, where large three-nucleon force effects are expected. It seems plausible that at higher energies, due to a rapid increase of a number of partial waves required to reach convergent results, a three-dimensional formulation of the Faddeev equations which avoids partial-wave decomposition is desirable.
Break-up channels in muon capture on He-3 (vol 90, 024001, 2014)
J. Golak, R. Skibiński, H. Witała, K. Topolnicki, AE. Elmeshneb, H. Kamada, A. Nogga, LE. Marcucci
abstract
Break-up channels in muon capture on He-3
J. Golak, R. Skibiński, H. Witała, K. Topolnicki, AE. Elmeshneb, H. Kamada, A. Nogga, LE. Marcucci
abstract
The mu(-) + H-2 -> nu(mu)+ n + n, mu(-) + He-3 -> nu(mu)+ H-3, mu(-) + He-3 -> nu(mu)+ n + d, and mu(-) + He-3 -> nu(mu) + n + n + p capture reactions are studied with various realistic potentials under full inclusion of final-state interactions. Our results for the two- and three-body break-up of He-3 are calculated with a variety of nucleon-nucleon potentials, among which is the AV18 potential, augmented by the Urbana IX three-nucleon potential. Most of our results are based on the single-nucleon weak-current operator. As a first step, we tested our calculation in the case of the mu(-) + H-2 -> nu(mu)+ n + n and mu(-) + He-3 -> nu(mu) + H-3 reactions, for which theoretical predictions obtained in a comparable framework are available. Additionally, we have been able to obtain for the first time a realistic estimate for the total rates of the muon capture reactions on 3He in the break-up channels: 544 s(-1) and 154 s(-1) for the n + d and n + n + p channels, respectively. Our results are compared with the most recent experimental data, finding a rough agreement for the total capture rates, but failing to reproduce the differential capture rates.
Investigation of the Three-Nucleon System Dynamics in the Deuteron-Proton Breakup Reaction
I. Ciepal, B. Klos, S. Kistryn, E. Stephan, A. Biegun, K. Bodek, A. Deltuva, E. Epelbaum, M. Eslami-Kalantari, AC. Fonseca, J. Golak, V. Jha, N. Kalantar-Nayestanaki, H. Kamada, G. Khatri, D. Kirillov, D. Kirillov, S. Kliczewski, A. Kozela, M. Kravcikova, H. Machner, A. Magiera, G. Martinska, J. Messchendorp, A. Nogga, W. Parol, A. Ramazani-Moghaddam-Arani, BJ. Roy, H. Sakai, K. Sekiguchi, I. Sitnik, R. Siudak, R. Skibiński, R. Sworst, J. Urban, H. Witała, J. Zejma
abstract
Precise and large sets of cross section, vector A (x) , A (y) and tensor A (xx) , A (xy) , A (yy) analyzing power data for the (1) H(d, pp)n breakup reactions were measured at 100 and 130 MeV deuteron beam energies with the SALAD and BINA detectors at KVI and the Germanium Wall setup at FZ-Julich. Results are compared with various theoretical approaches which model the three-nucleon system dynamics. The cross section data reveal a sizable three-nucleon force (3NF) and Coulomb force influence. In case of the analyzing powers very low sensitivity to these effects was found and the data are well describe by 2N models only. For A (xy) at 130 MeV, serious disagreements were observed when 3NF models are included in the calculations.
2N and 3N Systems in a Three Dimensional Formalism
K. Topolnicki, J. Golak, R. Skibiński, AE. Elmeshneb, H. Witała, A. Nogga, H. Kamada
abstract
We present an overview of our framework used to treat two- and three-nucleon (2N, 3N) systems employing three dimensional momentum eigenstates. Using a three dimensional formalism instead of the classical partial wave approach is an attractive alternative for a number of reasons, the most prominent being the very direct way of performing calculations. With the use of our tools it is possible to produce a working numerical realization of calculations in only a couple of steps from the fundamental (Schrodinger or Lippmann-Schwinger) equations. The FORTRAN implementations of the most complicated parts of the calculations are generated automatically by software that was written in our group. Additionally, at higher energies, three dimensional calculations avoid problems arising from slow convergence of partial wave decomposition based techniques. Our approach utilizes a very general form of the 2N and 3N forces and has been successfully used to obtain results for the 2N transition operator as well as for the 2N and 3N bound states (Golak et al. in Phys Rev C 81:034006, 2010; Few-Body Syst 53:237, 2012a; Few-Body Syst, 2012b).
Complete set of deuteron analyzing powers for dp elastic scattering at 250-294 MeV/nucleon and the three-nucleon force
K. Sekiguchi, Y. Wada, J. Miyazaki, H. Witała, M. Dozono, U. Gebauer, J. Golak, H. Kamada, S. Kawase, Y. Kubota, CS. Lee, Y. Maeda, T. Mashiko, K. Miki, A. Nogga, H. Okamura, T. Saito, H. Sakai, S. Sakaguchi, N. Sakamoto, M. Sasano, Y. Shimizu, R. Skibiński, H. Suzuki, T. Taguchi, K. Takahashi, TL. Tang, T. Uesaka, T. Wakasa, K. Yako
abstract
A complete high-precision set of deuteron analyzing powers for elastic deuteron-proton (dp) scattering at 250 and 294 MeV/nucleon has been measured. These data and previously existing data sets for the cross section at similar energies are compared to the results of three-nucleon Faddeev calculations based on modern nucleon-nucleon (NN) potentials alone or combined with two models of three-nucleon forces: the Tucson-Melbourne 99 and Urbana IX. Large discrepancies between pure NN theory and data, which are not resolved by the current three-nucleon forces, were found at c.m. backward angles theta(c.m.) greater than or similar to 120 degrees for all the deuteron analyzing powers and the cross section. Because only small relativistic effects were found for the deuteron analyzing powers and the cross section, the inclusion of short-range components of the three-nucleon force is probably required to get a better description of the data.
Spin-dependent cross sections from the three-body photodisintegration of He-3 at incident energies of 12.8 and 14.7 MeV
G. Laskaris, Q. Ye, B. Lalremruata, QJ. Ye, MW. Ahmed, T. Averett, A. Deltuva, D. Dutta, AC. Fonseca, H. Gao, J. Golak, M. Huang, HJ. Karwowski, JM. Mueller, LS. Myers, C. Peng, BA. Perdue, X. Qian, PU. Sauer, R. Skibiński, S. Stave, JR. Tompkins, HR. Weller, H. Witała, YK. Wu, Y. Zhang, W. Zheng
abstract
The first measurement of the three-body photodisintegration of polarized He-3 using a circularly polarized photon beam has been performed at incident energies of 12.8 and 14.7 MeV. This measurement was carried out at the high-intensity gamma-ray source located at Triangle Universities Nuclear Laboratory. A high-pressure He-3 target, polarized via spin exchange optical pumping with alkali metals, was used in the experiment. The spin-dependent double-and single-differential cross sections from (3)(He) over right arrow((gamma) over right arrow, n) pp for laboratory angles varying from 30 degrees to 165 degrees are presented and compared with state-of-the-art three-body calculations. The data reveal the importance of including the Coulomb interaction between protons in the three-body calculations.
Investigation of three nucleon force effects in deuteron-proton breakup reaction India
W. Parol, A. Kozela, I. Ciepal, B. Klos, K. Bodek, J. Golak, N. Kalantar-Nayestanaki, G. Khatri, S. Kistryn, P. Kulessa, A. Magiera, I. Mazumdar, J. Messchendorp, D. Rozpedzik, R. Skibiński, I. Skwira-Chalot, E. Stephan, H. Witała, A. Wronska, J. Zejma
abstract
Experimental study of the deuteron-proton breakup process was perfomed in KVI Groningen. In this paper current status of the collected data analysis is presented, including preliminary results of the cross section for the sample kinematical configuration.
Studies of the Three-Nucleon System Dynamics in the Deuteron-Proton Breakup Reaction
I. Ciepal, B. Klos, E. Stephan, S. Kistryn, A. Biegun, K. Bodek, A. Deltuva, E. Epelbaum, M. Eslami-Kalantari, AC. Fonseca, J. Golak, V. Jha, N. Kalantar-Nayestanaki, H. Kamada, G. Khatri, D. Kirillov, D. Kirillov, S. Kliczewski, A. Kozela, M. Kravcikova, H. Machner, A. Magiera, G. Martinska, J. Messchendorp, A. Nogga, W. Parol, A. Ramazani-Moghaddam-Arani, BJ. Roy, H. Sakai, K. Sekiguchi, I. Sitnik, R. Siudak, R. Skibinski, R. Sworst, J. Urban, H. Witala, J. Zejma
abstract
One of the most important goals of modern nuclear physics is to contruct nuclear force model which properly describes the experimental data. To develop and test predictions of current models the breakup 1H(d(->), pp)n reaction was investigated experimentally at 100 and 130 MeV deuteron beam energies. Rich set of data for cross section, vector and tensor analyzing powers was obtained with the use of the SALAD and BINA detectors at KVI and Germanium Wall setup at FZ-Julich. Results are compared with various theoretical approaches which describe the three-nucleon (3N) system dynamics. For correct description of the cross section data both, three-nucleon force (3NF) and Coulomb force, have to be included into calculations and influence of those ingredients is seizable at specific parts of the phase space. In case of the vector analyzing powers very low sensitivity to any effects beyond nucleon-nucleon interaction was found. At 130 MeV, the A(xy) data are not correctly described when 3NF models are included into calculations.
Investigation of three nucleon force effects in deuteron-proton breakup reaction India
W. Parol, A. Kozela, I. Ciepal, B. Klos, K. Bodek, J. Golak, N. Kalantar-Nayestanaki, G. Khatri, S. Kistryn, P. Kulessa, A. Magiera, I. Mazumdar, J. Messchendorp, D. Rozpedzik, R. Skibinski, I. Skwira-Chalot, E. Stephan, H. Witala, A. Wronska, J. Zejma
abstract
Experimental study of the deuteron-proton breakup process was perfomed in KVI Groningen. In this paper current status of the collected data analysis is presented, including preliminary results of the cross section for the sample kinematical configuration.
Muon induced deuteron disintegration in three-dimensions
K. Topolnicki, J. Golak, R. Skibiński, LE. Marcucci, H. Witała, AE. Elmeshneb
abstract
We present a three-dimensional (3D) description of muon induced deuteron disintegration. This reaction is treated as the decay of the muonic atom with the muon initially on the lowest K shell. Our aim is to calculate the total and differential decay rates. We work in momentum space and use 3D momentum eigenstates directly. This approach allowed us to calculate the appropriate nuclear matrix elements, necessary building blocks for the differential decay rate, in a single step. For contrast - in classical calculations many partial-waves have to be taken into account. We achieved a very good agreement between the 3D and partial-wave methods for calculations that involve single-nucleon currents. Our result for the total decay rate is also in agreement with experimental values, though these are not very precise. This success motivates us to also include two-nucleon current contributions that include the meson exchange currents. Additionally, our formalism can also be applied to other, so far poorly described, processes like: mu +(3) He -> + nu + n + d or mu +(3) He -> nu + n + n + p.
Studies of the Three-Nucleon System Dynamics in the Deuteron-Proton Breakup Reaction
I. Ciepal, B. Klos, E. Stephan, S. Kistryn, A. Biegun, K. Bodek, A. Deltuva, E. Epelbaum, M. Eslami-Kalantari, AC. Fonseca, J. Golak, V. Jha, N. Kalantar-Nayestanaki, H. Kamada, G. Khatri, D. Kirillov, D. Kirillov, S. Kliczewski, A. Kozela, M. Kravcikova, H. Machner, A. Magiera, G. Martinska, J. Messchendorp, A. Nogga, W. Parol, A. Ramazani-Moghaddam-Arani, BJ. Roy, H. Sakai, K. Sekiguchi, I. Sitnik, R. Siudak, R. Skibiński, R. Sworst, J. Urban, H. Witała, J. Zejma
abstract
One of the most important goals of modern nuclear physics is to contruct nuclear force model which properly describes the experimental data. To develop and test predictions of current models the breakup 1H(d(->), pp)n reaction was investigated experimentally at 100 and 130 MeV deuteron beam energies. Rich set of data for cross section, vector and tensor analyzing powers was obtained with the use of the SALAD and BINA detectors at KVI and Germanium Wall setup at FZ-Julich. Results are compared with various theoretical approaches which describe the three-nucleon (3N) system dynamics. For correct description of the cross section data both, three-nucleon force (3NF) and Coulomb force, have to be included into calculations and influence of those ingredients is seizable at specific parts of the phase space. In case of the vector analyzing powers very low sensitivity to any effects beyond nucleon-nucleon interaction was found. At 130 MeV, the A(xy) data are not correctly described when 3NF models are included into calculations.
Three-nucleon reactions with chiral dynamics
H. Witała, J. Golak, R. Skibiński, K. Topolnicki
abstract
Faddeev calculations using the chiral three-nucleon force at next-to-next-to-next-to-leading-order show that this force is not able to provide an explanation for the low-energy A(y) puzzle. Also the large discrepancies between data and theory for the symmetric-space-star and for the neutron-neutron quasi-free-scattering cross sections in low energy neutron-deuteron breakup cannot be explained by that three-nucleon force. The discrepancy for the neutron-neutron quasi-free-scattering cross section seems to require a modification of the S-1(0) neutron-neutron force.
Three-nucleon force in relativistic three-nucleon Faddeev calculations (vol 83, 044001, 2011)
H. Witała, J. Golak, R. Skibiński, W. Glockle, H. Kamada, WN. Polyzou
abstract
Calculations of Three-Nucleon Reactions
H. Witała, J. Golak, R. Skibiński, K. Topolnicki, H. Kamada, E. Epelbaum, W. Glockle, H. Krebs, WN. Polyzou, A. Nogga
abstract
Faddeev calculations using the chiral three-nucleon force in next-to-next-to-next-to-leading-order show that this force is too weak to provide an explanation for the low-energy A (y) puzzle. The large discrepancy between data and theory for the neutron-neutron quasi-free-scattering cross section in low energy neutron-deuteron breakup requires a modification of the neutron-neutron force. We discuss the consequences that a bound state of two neutrons has on neutron-deuteron scattering observables. At higher energies we compare the solutions of the non-relativistic three-nucleon Faddeev equations with three-nucleon force included to the solutions of its Poincar, invariant version.
Investigations of Few-Nucleon System Dynamics in Medium Energy Domain
I. Ciepal, B. Klos, S. Kistryn, E. Stephan, A. Biegun, K. Bodek, A. Deltuva, E. Epelbaum, M. Eslami-Kalantari, AC. Fonseca, J. Golak, V. Jha, N. Kalantar-Nayestanaki, H. Kamada, G. Khatri, D. Kirillov, D. Kirillov, S. Kliczewski, A. Kozela, M. Kravcikova, H. Machner, A. Magiera, G. Martinska, J. Messchendorp, A. Nogga, W. Parol, A. Ramazani-Moghaddam-Arani, BJ. Roy, H. Sakai, K. Sekiguchi, I. Sitnik, R. Siudak, R. Skibiński, R. Sworst, J. Urban, H. Witała, A. Wronska, J. Zejma
abstract
Precise and large set of cross sections, vector A (x) , A (y) and tensor A (xx) , A (xy) , A (yy) analyzing powers for the (1) H(d, pp)n breakup reactions were measured at 100 and 130 MeV deuteron beam energies with the use of the SALAD and BINA detectors at KVI and Germanium Wall setup at FZ-Julich. Results are compared with various theoretical approaches which model the three-nucleon (3N) system dynamics. The calculations are based on different two-nucleon (2N) potentials which can be combined with models of the three-nucleon force (3NF) and other pieces of the dynamics can also be included like the Coulomb interaction and relativistic effects. The cross sections data reveal seizable 3NF and Coulomb force influence. In case of analyzing powers very low sensitivity to the effects was found and the data are well describe by 2N models only. At 130 MeV for A (xy) serious disagreements appear when 3NF models are included into calculations.
H-3 at Next-to-Next-to-Next-to Leading Order of the Chiral Expansion
R. Skibiński, J. Golak, K. Topolnicki, H. Witała, E. Epelbaum, W. Glockle, H. Krebs, H. Kamada, A. Nogga
abstract
The chiral three-nucleon force (3NF) at next-to-next-to-next-to leading order ((NLO)-L-3) is used to calculate the triton wave function and the doublet nucleon-deuteron scattering length. This allows us to fix the values of the low-energy constants which are free parameters of the theory. The obtained values of these parameters, the expectation values of the kinetic energy, two- and three-body potentials and individual contributions of different parts of 3NF are given.
First Measurements of Spin-Dependent Double-Differential Cross Sections and the Gerasimov-Drell-Hearn Integrand from (3)(H)over-right-arrowe((gamma)over-right-arrow, n)pp at Incident Photon Energies of 12.8 and 14.7 MeV
G. Laskaris, Q. Ye, B. Lalremruata, QJ. Ye, MW. Ahmed, T. Averett, A. Deltuva, D. Dutta, AC. Fonseca, H. Gao, J. Golak, M. Huang, HJ. Karwowski, JM. Mueller, LS. Myers, C. Peng, BA. Perdue, X. Qian, PU. Sauer, R. Skibiński, S. Stave, JR. Tompkins, HR. Weller, H. Witała, YK. Wu, Y. Zhang, W. Zheng
abstract
The first measurement of the three-body photodisintegration of longitudinally polarized He-3 with a circularly polarized gamma-ray beam was carried out at the High Intensity gamma-ray Source facility located at Triangle Universities Nuclear Laboratory. The spin-dependent double-differential cross sections and the contributions from the three-body photodisintegration to the He-3 Gerasimov-Drell-Hearn integrand are presented and compared with state-of-the-art three-body calculations at the incident photon energies of 12.8 and 14.7 MeV. The data reveal the importance of including the Coulomb interaction between protons in three-body calculations.
SYSTEMATIC STUDIES OF THE THREE-NUCLEON SYSTEM DYNAMICS IN THE DEUTRON-PROTON BREAKUP REACTION
B. Klos, I. Ciepal, S. Kistryn, E. Stephan, A. Biegun, K. Bodek, A. Deltuva, E. Epelbaum, M. Eslami-Kalantari, AC. Fonseca, J. Golak, B. Jamroz, V. Jha, N. Kalantar-Nayestanaki, H. Kamada, G. Khatri, D. Kirillov, D. Kirillov, S. Kliczewski, A. Kozela, M. Kravcikova, H. Machner, A. Magiera, G. Martinska, J. Messchendorp, A. Nogga, W. Parol, A. Ramazani-Moghaddam-Arani, BJ. Roy, H. Sakai, K. Sekiguchi, I. Sitnik, R. Siudak, R. Skibinski, R. Sworst, J. Urban, H. Witala, A. Wronska, J. Zejma
abstract
Precise and large sets of data for cross section, vector and tensor analyzing powers for the H-1((d) over right arrow ,pp)n breakup reaction were obtained in experiments carried out at KVI Groningen and FZ-Julich at deuteron beam energies of 100 MeV, 13 MeV and 160 MeV (cross sections only). These precise experimental data obtained in a wide phase-space region allowed to establish evidences for three-nucleon force contributions and to confirm predictions of sizable effect of the Coulomb force. The vector analyzing powers data are generally quite well described by theoretical predictions even with pure nucleon nucleon interactions. Tensor analyzing powers can be also very well reproduced by calculations in most of the studied region but in some regions locally discrepancies are observed at energy of 130 MeV. DOI:10.5506/APhysPolB.44.345
SYSTEMATIC STUDIES OF THE THREE-NUCLEON SYSTEM DYNAMICS IN THE DEUTRON-PROTON BREAKUP REACTION
B. Klos, I. Ciepal, S. Kistryn, E. Stephan, A. Biegun, K. Bodek, A. Deltuva, E. Epelbaum, M. Eslami-Kalantari, AC. Fonseca, J. Golak, B. Jamroz, V. Jha, N. Kalantar-Nayestanaki, H. Kamada, G. Khatri, D. Kirillov, D. Kirillov, S. Kliczewski, A. Kozela, M. Kravcikova, H. Machner, A. Magiera, G. Martinska, J. Messchendorp, A. Nogga, W. Parol, A. Ramazani-Moghaddam-Arani, BJ. Roy, H. Sakai, K. Sekiguchi, I. Sitnik, R. Siudak, R. Skibiński, R. Sworst, J. Urban, H. Witała, A. Wronska, J. Zejma
abstract
Precise and large sets of data for cross section, vector and tensor analyzing powers for the H-1((d) over right arrow ,pp)n breakup reaction were obtained in experiments carried out at KVI Groningen and FZ-Julich at deuteron beam energies of 100 MeV, 13 MeV and 160 MeV (cross sections only). These precise experimental data obtained in a wide phase-space region allowed to establish evidences for three-nucleon force contributions and to confirm predictions of sizable effect of the Coulomb force. The vector analyzing powers data are generally quite well described by theoretical predictions even with pure nucleon nucleon interactions. Tensor analyzing powers can be also very well reproduced by calculations in most of the studied region but in some regions locally discrepancies are observed at energy of 130 MeV. DOI:10.5506/APhysPolB.44.345
Vector analyzing powers of the deuteron-proton elastic scattering and breakup at 100 MeV
E. Stephan, S. Kistryn, A. Biegun, K. Bodek, I. Ciepal, A. Deltuva, M. Eslami-Kalantari, AC. Fonseca, I. Gasparic, J. Golak, L. Joulaeizadeh, N. Kalantar-Nayestanaki, H. Kamada, B. Klos, A. Kozela, JG. Messchendorp, H. Moeini, A. Nogga, W. Parol, A. Ramazani-Moghaddam-Arani, R. Skibiński, R. Sworst, A. Wilczek, H. Witała, J. Zejma
abstract
High-quality vector analyzing power data for the H-1(d,pp)n breakup reaction and elastic scattering at 100 MeV beam energy have been measured in a large part of the phase space for these processes. The results are compared to theoretical predictions obtained using the charge-dependent Bonn potential alone or combined with the three-nucleon force TM99 as well as to the results of calculations in the coupled-channel approach, with or without the inclusion of the Coulomb interaction. In the studied observables, effects of the 3NF and the Coulomb force are almost absent. The pairwise NN interactions alone are sufficient to describe the experimental results.
Different Methods for the Two-Nucleon T-Matrix in the Operator Form
J. Golak, R. Skibiński, H. Witała, K. Topolnicki, W. Glockle, A. Nogga, H. Kamada
abstract
We compare three methods to calculate the nucleon-nucleon t-matrix based on the three-dimensional formulation of Golak et al. (Phys Rev C 81:034006, 2010). In the first place we solve a system of complex linear inhomogeneous equations directly for the t-matrix. Our second method is based on iterations and a variant of the Lanczos algorithm. In the third case we obtain the t-matrix in two steps, solving a system of real linear equations for the k-matrix expansion coefficients and then solving an on-shell equation, which connects the scalar coefficients of the k- and t-matrices. A very good agreement among the three methods is demonstrated for selected nucleon-nucleon scattering observables using a chiral next-to-next-to-leading-order neutron-proton potential. We also apply our three-dimensional framework to the demanding problem of proton-proton scattering, using a corresponding version of the nucleon-nucleon potential and supplementing it with the (screened) Coulomb force, taken also in the three-dimensional form. We show converged results for two different screening functions and find a very good agreement with other methods dealing with proton-proton scattering.
The Complex Energy Method Applied to the Nd Scattering with a Model Three-Body Force
AM. Phyu, H. Kamada, J. Golak, HH. Oo, H. Witała, W. Glockle
abstract
Using the complex energy method, the problem of nucleon-deuteron scattering is solved with a simple three-body force having a separable form. Our results are compared with the results of modern direct two-variable calculations and a good agreement is found. This forms a firm base for other applications of the complex energy method.
Studies of the Three-Nucleon System Dynamics in the Deuteron-Proton Breakup Reaction
I. Ciepal, B. Klos, S. Kistryn, E. Stephan, A. Biegun, K. Bodek, A. Deltuva, E. Epelbaum, M. Eslami-Kalantari, AC. Fonseca, J. Golak, V. Jha, N. Kalantar-Nayestanaki, H. Kamada, G. Khatri, D. Kirillov, D. Kirillov, S. Kliczewski, A. Kozela, M. Kravcikova, H. Machner, A. Magiera, G. Martinska, J. Messchendorp, A. Nogga, W. Parol, A. Ramazani-Moghaddam-Arani, BJ. Roy, H. Sakai, K. Sekiguchi, I. Sitnik, R. Siudak, R. Skibinski, R. Sworst, J. Urban, H. Witala, A. Wronska, J. Zejma
abstract
Precise and large sets of cross sections for the H-1(d,pp)n and H-2(p,pp)n breakup reactions were measured at 130 deuteron and 190 MeV proton beam energies with the use of detectors which covered almost the full phase space. The results are compared with various theoretical approaches which model the 3N system dynamics. The calculations are based on different 2N potentials which can be combined with models of the three-nucleon force (3NF). The differential cross sections appear to be a very sensitive tool for testing the interaction models and allow to search for various ingredients of the dynamics, not only the 3NF but also the Coulomb interaction and relativistic effects which are relatively new achievements of the theory.
Studies of the Three-Nucleon System Dynamics in the Deuteron-Proton Breakup Reaction
I. Ciepal, B. Klos, S. Kistryn, E. Stephan, A. Biegun, K. Bodek, A. Deltuva, E. Epelbaum, M. Eslami-Kalantari, AC. Fonseca, J. Golak, V. Jha, N. Kalantar-Nayestanaki, H. Kamada, G. Khatri, D. Kirillov, D. Kirillov, S. Kliczewski, A. Kozela, M. Kravcikova, H. Machner, A. Magiera, G. Martinska, J. Messchendorp, A. Nogga, W. Parol, A. Ramazani-Moghaddam-Arani, BJ. Roy, H. Sakai, K. Sekiguchi, I. Sitnik, R. Siudak, R. Skibiński, R. Sworst, J. Urban, H. Witała, A. Wronska, J. Zejma
abstract
Precise and large sets of cross sections for the H-1(d,pp)n and H-2(p,pp)n breakup reactions were measured at 130 deuteron and 190 MeV proton beam energies with the use of detectors which covered almost the full phase space. The results are compared with various theoretical approaches which model the 3N system dynamics. The calculations are based on different 2N potentials which can be combined with models of the three-nucleon force (3NF). The differential cross sections appear to be a very sensitive tool for testing the interaction models and allow to search for various ingredients of the dynamics, not only the 3NF but also the Coulomb interaction and relativistic effects which are relatively new achievements of the theory.
Two-body photodisintegration of He-3 between 7 and 16 MeV
W. Tornow, HJ. Karwowski, JH. Kelley, R. Raut, G. Rusev, SC. Stave, AP. Tonchev, A. Deltuva, AC. Fonseca, LE. Marcucci, M. Viviani, A. Kievsky, J. Golak, R. Skibiński, H. Witała, R. Schiavilla
abstract
A comprehensive data set is reported for the two-body photodisintegration cross section of He-3 using mono-energetic photon beams at eleven energies between 7.0 and 16.0 MeV. A He-3 + Xe high-pressure gas scintillator served as target and detector. Although our data are in much better agreement with our state-of-the-art theoretical calculations than the majority of the previous data, these calculations underpredict the new data by about 10%. This disagreement suggests an incomplete understanding of the dynamics of the three-nucleon system and its response to electromagnetic probes. (C) 2011 Elsevier B.V. All rights reserved.
Signatures of the chiral two-pion exchange electromagnetic currents in the H-2 and He-3 photodisintegration reactions
D. Rozpedzik, J. Golak, S. Kolling, E. Epelbaum, R. Skibiński, H. Witała, H. Krebs
abstract
The recently derived long-range two-pion exchange (TPE) contributions to the nuclear current operator that appear at next-to-leading order (NLO) of the chiral expansion are used to describe electromagnetic processes. We study their role in the photodisintegration of H-2 and He-3 and compare our predictions with the experimental data. The bound and scattering states are calculated using five different parametrizations of the chiral next-to-next-to-leading order ((NLO)-L-2) nucleon-nucleon (NN) potential, which allows us to estimate the theoretical uncertainty at a given order in the chiral expansion. For some observables the results are very close to the predictions based on the AV18 NN potential and the current operator (partly) consistent with this force. In most cases, the addition of long-range TPE currents improved the description of the experimental data.
Three nucleon force effects in intermediate-energy deuteron analyzing powers for dp elastic scattering
K. Sekiguchi, H. Okamura, N. Sakamoto, H. Suzuki, M. Dozono, Y. Maeda, T. Saito, S. Sakaguchi, H. Sakai, M. Sasano, Y. Shimizu, T. Wakasa, K. Yako, H. Witała, W. Glockle, J. Golak, H. Kamada, A. Nogga
abstract
A complete high precision set of deuteron analyzing powers for elastic deuteron- proton (dp) scattering at 250 MeV/nucleon (MeV/N) has been measured. The new data are presented together with data from previous measurements at 70, 100, 135 and 200 MeV/N. They are compared with the results of three- nucleon (3N) Faddeev calculations based on modern nucleon- nucleon (NN) potentials alone or combined with two models of three nucleon forces (3NFs): the Tucson-Melbourne 99 (TM99) and Urbana IX. At 250 MeV/N large discrepancies between pure NN models and data, which are not resolved by including 3NFs, were found at c. m. backward angles of theta(c.m). greater than or similar to 120 degrees for almost all the deuteron analyzing powers. These discrepancies are quite similar to those found for the cross section at the same energy. We found small relativistic effects that cannot resolve the discrepancies with the data indicating that other, short- ranged 3NFs are required to obtain a proper description of the data.
Vector and Tensor Analyzing Powers in Deuteron-Proton Breakup
E. Stephan, S. Kistryn, N. Kalantar-Nayestanaki, A. Biegun, K. Bodek, I. Ciepal, A. Deltuva, M. Eslami-Kalantari, AC. Fonseca, I. Gasparic, J. Golak, B. Jamroz, L. Joulaeizadeh, H. Kamada, M. Kis, B. Klos, A. Kozela, M. Mahjour-Shafiei, H. Mardanpour, J. Messchendorp, A. Micherdzinska, H. Moeini, A. Nogga, A. Ramazani-Moghaddam-Arani, R. Skibiński, R. Sworst, H. Witała, J. Zejma
abstract
High precision data for vector and tensor analyzing powers of the (1)H (d(->), pp)nbreakup reaction at 130 and 100 MeV deuteron beam energies have been measured in a large fraction of the phase space. They are compared to the theoretical predictions based on various approaches to describe the three nucleon (3N) system dynamics. Theoretical predictions describe very well the vector analyzing power data, with no need to include any three-nucleon force effects for these observables. Tensor analyzing powers can be also very well reproduced by calculations in most of the studied region, but locally certain discrepancies are observed. At 130 MeV for A (xy) such discrepancies usually appear, or are enhanced, when model 3N forces are included. Predicted effects of 3NFs are much lower at 100 MeV and at this energy equally good consistency between the data and the calculations is obtained with or without 3NFs.
Determination of Wolfenstein Parameters in NN Scattering Directly from Observables
H. Kamada, W. Glockle, H. Witała, J. Golak, R. Skibiński
abstract
The Wolfenstein parameters are for the first time obtained analytically in terms of observables. It is shown that a set of ten nucleon-nucleon (NN) observables, which contains polarization observables together with the differential cross section, determines uniquely the solution for Wolfenstein parameters except for a common insignificant phase. Using such analytical solutions one expects to get more accurate theoretical parameters for the potential models by chi (2) fitting to the resulting Wolfenstein parameter data than the standard manner of a phase-shift analysis. An example of fixing a unique set of physical solutions for the Wolfenstein parameters from a set of 16 solutions based on nine observables alone and adding one more observable is illustrated using pseudo data generated by the CD Bonn potential.
Recent Developments of a Three-dimensional Description of the NN System
R. Skibiński, J. Golak, D. Rozpedzik, K. Topolnicki, H. Witała, W. Glockle, A. Nogga, E. Epelbaum, H. Kamada, C. Elster, I. Fachruddin
abstract
A recently developed three-dimensional formulation of nucleon-nucleon (NN) scattering is briefly presented. Here the NN t-matrix is represented by six spin-momentum operators accompanied by six scalar functions of momentum vectors. A numerical example for the NN scattering cross section is given.
Three-nucleon force in relativistic three-nucleon Faddeev calculations
H. Witała, J. Golak, R. Skibiński, W. Glockle, H. Kamada, WN. Polyzou
abstract
We extend our formulation of relativistic three-nucleon Faddeev equations to include both pairwise interactions and a three-nucleon force. Exact Poincare invariance is realized by adding interactions to the mass Casimir operator (rest Hamiltonian) of the noninteracting system without changing the spin Casimir operator. This is achieved by using interactions defined by rotationally invariant kernels that are functions of internal momentum variables and single-particle spins that undergo identical Wigner rotations. To solve the resulting equations one needs matrix elements of the three-nucleon force with these properties in a momentum-space partial-wave basis. We present two methods to calculate matrix elements of three-nucleon forces with these properties. For a number of examples we show that at higher energies, where effects of relativity and of three-nucleon forces are non-negligible, a consistent treatment of both is required to properly analyze the data.
The Tucson-Melbourne three-nucleon force in the automatized partial-wave decomposition
R. Skibiński, J. Golak, K. Topolnicki, H. Witała, H. Kamada, W. Glockle, A. Nogga
abstract
A recently developed procedure for a partial-wave decomposition of a three-nucleon force is applied to the pi-pi, pi-rho and rho-rho components of the Tucson-Melbourne three-nucleon potential. The resulting matrix elements for the pi-pi and pi-rho components are compared with the values obtained using the standard approach to the partial-wave decomposition, in which the pi-rho expressions for the matrix elements are also derived and presented. Several numerical tests and results for the triton binding energy and the correlation function prove the reliability and efficiency of the new method.
Mini Review of Poincar, Invariant Quantum Theory
WN. Polyzou, C. Elster, W. Glockle, J. Golak, Y. Huang, H. Kamada, R. Skibiński, H. Witała
abstract
We review the construction and applications of exactly Poincar, invariant quantum mechanical models of few-degree of freedom systems. We discuss the construction of dynamical representations of the Poincar, group on few-particle Hilbert spaces, the relation to quantum field theory, the formulation of cluster properties, and practical considerations related to the construction of realistic interactions and the solution of the dynamical equations. Selected applications illustrate the utility of this approach.
Relativistic Effects in Neutron-Deuteron Elastic Scattering and Breakup
H. Witała, J. Golak, R. Skibiński, W. Glockle, WN. Polyzou, H. Kamada
abstract
We solved the Faddeev equation in a Poincar, invariant model of the three-nucleon system. Two-body interactions are generated so that when they are added to the two-nucleon invariant mass operator (rest energy) the two-nucleon S matrix is identical to the experimental S matrix modeled with a given nucleon-nucleon interaction. Cluster properties of the three-nucleon S-matrix determine how these two-nucleon interactions are embedded in the three-nucleon mass operator. Differences in the predictions of the relativistic and corresponding non-relativistic models for elastic and breakup processes are investigated. Of special interest are effects of relativity on the elastic scattering angular distribution and total cross sections, the lowering of the A (y) maximum in elastic nucleon-deuteron (Nd) scattering below a parts per thousand 25 MeV caused by the Wigner spin rotations and the significant changes of the breakup cross sections in certain regions of the phase-space.
Momentum space 3N Faddeev calculations of hadronic and electromagnetic reactions with proton-proton Coulomb and three-nucleon forces included
H. Witała, R. Skibiński, J. Golak, W. Glockle
abstract
We extend our approach to incorporate the proton-proton (pp) Coulomb force into the three-nucleon (3N) momentum space Faddeev calculations of elastic proton-deuteron (pd) scattering and breakup to the case when also a three-nucleon force (3NF) is acting. In addition, we formulate that approach in the application to electron-and gamma-induced reactions on He-3. The main new ingredient is a 3-dimensional screened pp Coulomb t-matrix obtained by a numerical solution of a 3-dimensional Lippmann-Schwinger equation (LSE). The resulting equations have the same structure as the Faddeev equations which describe pd scattering without 3NF acting. That shows the practical feasibility of both presented formulations.
Complete Set of Deuteron Analyzing Powers for Deuteron Proton Elastic Scattering at 250 MeV/nucleon and Three-Nucleon Forces
K. Sekiguchi, H. Okamura, N. Sakamoto, H. Suzuki, M. Dozono, Y. Maeda, T. Saito, S. Sakaguchi, H. Sakai, M. Sasano, Y. Shimizu, T. Wakasa, K. Yako, H. Witała, W. Glockle, J. Golak, H. Kamada, A. Nogga
abstract
Measurements of a complete set of deuteron analyzing powers (iT(11), T-20, T-21, and T-22) for elastic deuteron proton scattering at 250 MeV/nucleon have been performed with polarized deuteron beams at RIKEN RI Beam Factory. The obtained data are compared with Faddeev calculations based on the modern nucleon nucleon forces together with the Tucson-Melbourne'99 and UrbanaIX three-nucleon forces.
Vector and tensor analyzing powers in deuteron-proton breakup at 130 MeV
E. Stephan, S. Kistryn, R. Sworst, A. Biegun, K. Bodek, I. Ciepal, A. Deltuva, E. Epelbaum, AC. Fonseca, J. Golak, N. Kalantar-Nayestanaki, H. Kamada, M. Kis, B. Klos, A. Kozela, M. Mahjour-Shafiei, A. Micherdzinska, A. Nogga, R. Skibiński, H. Witała, A. Wronska, J. Zejma, W. Zipper
abstract
High-precision data for vector and tensor analyzing powers for the H-1((d) over right arrow, pp)n reaction at a 130-MeV deuteron beam energy have been measured over a large part of the phase space. Theoretical predictions based on various approaches to describe the three nucleon (3N) system reproduce very well the vector analyzing power data and no three-nucleon force effect is observed for these observables. Tensor analyzing powers are also very well reproduced by calculations in almost the whole studied region, but locally certain discrepancies are observed. For A(xy) such discrepancies usually appear, or are enhanced, when model 3N forces, TM99 or Urbana, are included. Problems of all theoretical approaches with describing A(xx) and A(yy) are limited to very small kinematical regions, usually characterized by the lowest energy of the relative motion of the two protons.
Vector and tensor analyzing powers in deuteron-proton breakup at 130 MeV
E. Stephan, S. Kistryn, R. Sworst, A. Biegun, K. Bodek, I. Ciepal, A. Deltuva, E. Epelbaum, AC. Fonseca, J. Golak, N. Kalantar-Nayestanaki, H. Kamada, M. Kis, B. Klos, A. Kozela, M. Mahjour-Shafiei, A. Micherdzinska, A. Nogga, R. Skibinski, H. Witala, A. Wronska, J. Zejma, W. Zipper
abstract
High-precision data for vector and tensor analyzing powers for the H-1((d) over right arrow, pp)n reaction at a 130-MeV deuteron beam energy have been measured over a large part of the phase space. Theoretical predictions based on various approaches to describe the three nucleon (3N) system reproduce very well the vector analyzing power data and no three-nucleon force effect is observed for these observables. Tensor analyzing powers are also very well reproduced by calculations in almost the whole studied region, but locally certain discrepancies are observed. For A(xy) such discrepancies usually appear, or are enhanced, when model 3N forces, TM99 or Urbana, are included. Problems of all theoretical approaches with describing A(xx) and A(yy) are limited to very small kinematical regions, usually characterized by the lowest energy of the relative motion of the two protons.
NUMERICAL INVESTIGATIONS OF THE THREE-DIMENSIONAL PROTON-PROTON SCREENED COULOMB t-MATRIX
R. Skibiński, J. Golak, H. Witała
abstract
We demonstrate behaviour of the momentum space screened Coulomb t-matrix, obtained by a numerical solution of the three-dimensional Lippmann-Schwinger equation. Examples are given for different types of screening. They prove that it is possible to obtain numerically a reliable three-dimensional screened Coulomb t-matrix, what is important in view of its application in few-body calculations.
3N scattering in a three-dimensional operator formulation
W. Glockle, I. Fachruddin, C. Elster, J. Golak, R. Skibiński, H. Witała
abstract
A recently developed formulation for a direct treatment of the equations for two-and three-nucleon bound states as set of coupled equations of scalar functions depending only on vector momenta is extended to three-nucleon scattering. Starting from the spin-momentum dependence occurring as scalar products in two-and three-nucleon forces together with other scalar functions, we present the Faddeev multiple scattering series in which order by order the spin degrees can be treated analytically leading to 3D integrations over scalar functions depending on momentum vectors only. Such formulation is especially important in view of awaiting extension of 3N Faddeev calculations to projectile energies above the pion production threshold and applications of chiral perturbation theory 3N forces, which are to be most efficiently treated directly in such three-dimensional formulation without having to expand these forces into a partial-wave basis.
Two-nucleon systems in three dimensions
J. Golak, W. Glockle, R. Skibiński, H. Witała, D. Rozpedzik, K. Topolnicki, I. Fachruddin, C. Elster, A. Nogga
abstract
A recently developed formulation for treating two- and three-nucleon bound states in a three-dimensional formulation based on spin-momentum operators is extended to nucleon-nucleon scattering. Here the nucleon-nucleon T-matrix is represented by six spin-momentum operators accompanied by six scalar functions of momentum vectors. We present the formulation and provide numerical examples for the deuteron and nucleon-nucleon scattering observables. A comparison to results from a standard partial-wave decomposition establishes the reliability of this formulation.
A new way to perform partial-wave decompositions of few-nucleon forces
J. Golak, D. Rozpedzik, R. Skibiński, K. Topolnicki, H. Witała, W. Glockle, A. Nogga, E. Epelbaum, H. Kamada, C. Elster, I. Fachruddin
abstract
We formulate a general and exact method of partial-wave decomposition (PWD) of any nucleon-nucleon (NN) potential and any three-nucleon (3N) force. The approach allows one to efficiently use symbolic algebra software to generate the interaction-dependent part of the program code calculating the interaction. We demonstrate the feasibility of this approach for the one-boson exchange BonnB potential, a recent nucleon-nucleon chiral force and the chiral two-pion-exchange three-nucleon force. In all cases very good agreement between the new and the traditional PWD is found. The automated PWD offered by the new approach is of the utmost importance in view of future applications of numerous chiral N3LO contributions to the 3N force in three-nucleon calculations.
The Exact Three-Dimensional Half-Shell t-Matrix for a Sharply Cut-off Coulomb Potential in the Screening Limit
W. Glockle, J. Golak, R. Skibiński, H. Witała
abstract
The screening limit of the three-dimensional half-shell t-matrix for a sharply cut-off Coulomb potential is analytically derived without reference to partial wave expansion. The numerical solutions of the three-dimensional Lippmann-Schwinger equation for increasing cut-off radii provide half-shell t-matrices which are in quite a good agreement with the asymptotic values.
A New Treatment of 2N and 3N Bound States in Three Dimensions
W. Glockle, C. Elster, J. Golak, R. Skibiński, H. Witała, H. Kamada
abstract
The direct treatment of the Faddeev equation for the three-boson system in 3 dimensions is generalized to nucleons. The one Faddeev equation for identical bosons is replaced by a strictly finite set of coupled equations for scalar functions which depend only on 3 variables. The spin-momentum dependence occurring as scalar products in 2N and 3N forces accompanied by scalar functions is supplemented by a corresponding expansion of the Faddeev amplitudes. After removing the spin degrees of freedom by suitable operations only scalar expressions depending on momenta remain. The corresponding steps are performed for the deuteron leading to two coupled equations.
Investigation of the Exclusive He-3(e, e ' pn)H-1 Reaction
DG. Middleton, JRM. Annand, MA. Antelo, C. Ayerbe, P. Barneo, D. Baumann, J. Bermuth, J. Bernauer, HP. Blok, R. Bohm, D. Bosnar, M. Ding, MO. Distler, J. Friedrich, JG. Llongo, DI. Glazier, J. Golak, W. Glockle, P. Grabmayr, T. Hehl, J. Heim, WHA. Hesselink, E. Jans, H. Kamada, GJ. Manas, M. Kohl, L. Lapikas, IJD. MacGregor, I. Martin, JC. McGeorge, H. Merkel, P. Merle, K. Monstad, F. Moschini, U. Muller, A. Nogga, R. Perez-Benito, T. Pospischil, M. Potokar, G. Rosner, M. Seimetz, R. Skibiński, H. de Vries, T. Walcher, DP. Watts, M. Weinriefer, M. Weiss, H. Witała, B. Zihlmann
abstract
Cross sections for the He-3(e, e' pn)H-1 reaction were measured for the first time at energy transfers of 220 and 270 MeV for several momentum transfers ranging from 300 to 450 MeV/c. Cross sections are presented as a function of the momentum of the recoil proton and the momentum transfer. Continuum Faddeev calculations using the Argonne V18 and Bonn-B nucleon-nucleon potentials overestimate the measured cross sections by a factor 5 at low recoil proton momentum with the discrepancy becoming smaller at higher recoil proton momentum.
Precise set of tensor analyzing power T-20 data for the deuteron-proton breakup at 130 MeV
E. Stephan, S. Kistryn, A. Biegun, K. Bodek, I. Ciepal, A. Deltuva, E. Epelbaum, AC. Fonseca, J. Golak, N. Kalantar-Nayestanaki, H. Kamada, M. Kis, B. Klos, A. Kozela, M. Mahjour-Shafiei, A. Micherdzinska, A. Nogga, R. Skibiński, R. Sworst, H. Witała, J. Zejma, W. Zipper
abstract
High-precision tensor analyzing power T-20 data of the H-1(d, pp)n reaction at 130 MeV beam energy have been determined for 81 kinematical configurations. They are compared to theoretical predictions based on various approaches to describe the dynamics of the three-nucleon (3N) system. The calculations are performed using modern realistic nucleon-nucleon potentials combined with three-nucleon force (3NF) models or with an effective 3NF resulting from the explicit treatment of the Delta-isobar in coupled-channels (CC) calculations. Alternatively, the framework of chiral perturbation theory is used to generate consistent two-nucleon and three-nucleon potentials at the currently numerically attainable order. Results of the CC calculations with the Delta degrees of freedom and including long-range Coulomb force are also shown. In general all predictions are consistent with each other and describe the experimental T-20 results quite well. In a few configurations small inconsistencies between the data and the results of all approaches are observed. Predicted effects of the 3NF are not big and in most cases do not lead to an improved description of the data. The Coulomb force effects are also small in size and often opposite to the effects of TM99 3NF.
A novel treatment of the proton-proton Coulomb force in proton-deuteron Faddeev calculations: Elastic scattering
H. Witała, R. Skibiński, J. Golak, W. Glockle
abstract
We propose a novel approach to incorporate the proton-proton (pp) Coulomb force into the three-nucleon (3N) Faddeev calculations. The main new ingredient is a 3-dimensional screened pp Coulomb t -matrix obtained by a numerical solution of the 3-dimensional Lippmann-Schwinger (LS) equation. We demonstrate numerically and provide analytical insight that the elastic proton-deuteron (pd ) observables can be determined directly from the resulting on-shell 3N amplitude increasing the screening radius. The screening limit exists without the need of renormalisation not only for observables but for the elastic pd amplitude itself.
A novel treatment of the proton-proton Coulomb force in proton-deuteron Faddeev calculations: Breakup
H. Witała, R. Skibiński, J. Golak, W. Glockle
abstract
We extend our approach to incorporate the proton-proton (ppCoulomb force into the three-nucleon (3NFaddeev calculations from elastic proton-deuteron (pdscattering to the breakup process. The main new ingredient is a 3-dimensional screened pp Coulomb t -matrix obtained by a numerical solution of the 3-dimensional Lippmann-Schwinger (LS) equation. We demonstrate numerically that the proton-deuteron (pdbreakup observables can be determined from the resulting on-shell 3N amplitudes increasing the screening radius. However, contrary to the pd elastic scattering, the screening limit exists only after renormalisation of the pp t -matrices.
Testing nucleonic forces with three nucleon reactions
H. Witała, J. Golak, R. Skibiński, W. Glockle, H. Kamada, A. Nogga
abstract
Results on nucleon-deuteron (Nd) elastic scattering and deuteron breakup below the pion production threshold are discussed emphasizing the need for a three-nucleon force (3NF). Precise solutions of the three-nucleon (3N) Faddeev equations with realistic (semi) phenomenological nucleon-nucleon (NN) potentials alone are insufficient to describe the data. Results involving in addition standard 3NF models like the 2 pi-exchange TM99 force are presented, which, however, are usually insufficient as well. Relativistic effects turn out to be small. These two observations point to the need of short range 3NF components. Chiral perturbation theory (chi PT) provides 3NF's which go beyond the 2 pi-exchange including a one -pi-exchange-contact force and a pure 3N-contact force at the lowest order of their occurrence. Their application at the higher energies yields results which are qualitatively and quantitatively different from the results of the standard NN and 3NF models. Though somewhat stretched beyond their proper domain of applicability of that type of forces this supports the conclusion of an increased importance of short range 3NF's at those higher energies. The consistent chi PT forces carried to higher orders can be expected to establish the final form of the nuclear Hamiltonian.
Proton-proton scattering without Coulomb force renormalization
R. Skibiński, J. Golak, H. Witała, W. Glockle
abstract
We demonstrate numerically that proton-proton (pp) scattering observables can be determined directly by standard short-range methods using a screened pp Coulomb force without renormalization. In the examples the appropriate screening radii are given. We also numerically investigate solutions of the 3-dimensional Lippmann-Schwinger (LS) equation for a screened Coulomb potential alone in the limit of large screening radii and confirm analytically predicted properties for off-shell, half-shell and on-shell Coulomb t-matrices. These 3-dimensional solutions will form a basis for a novel approach to include the pp Coulomb interaction into the 3N Faddeev framework.
Three-nucleon force effects in the H-1(d,pp)n reaction at 135 MeV/nucleon
K. Sekiguchi, H. Sakai, H. Witała, W. Glockle, J. Golak, K. Itoh, H. Kamada, T. Kawabata, H. Kuboki, Y. Maeda, A. Nogga, H. Okamura, S. Sakaguchi, N. Sakamoto, Y. Sasamoto, M. Sasano, R. Skibiński, K. Suda, Y. Takahashi, T. Uesaka, T. Wakasa, K. Yako
abstract
The deuteron to proton polarization transfer coefficients K-yy(y') and K-y(y') together with the deuteron analyzing powers are measured in three coplanar configurations of the deuteron-proton breakup reaction with a 135-MeV/nucleon polarized deuteron beam at the RIKEN Accelerator Research Facility. The data are compared with theoretical predictions based on exact solutions of the three-nucleon (3N) Faddeev equations with high-precision nucleon-nucleon (NN) forces, alone or combined with two 3N force (3NF) models, the 2 pi-exchange Tucson-Melbourne(')(99) (TM(')99) and Urbana IX. Large 3NF effects have been found for all the measured observables. Predicted effects are supported by the data, with the exception of the vector analyzing power A(y)(d). For this observable, theory based on only NN forces is sufficient to explain the data. The behavior of the breakup analyzing powers is found to be different from the corresponding observables in elastic nucleon-deuteron scattering.
LORENTZ BOOSTED NUCLEON-NUCLEON T-MATRIX AND THE TRITON BINDING ENERGY
H. Kamada, W. Glockle, H. Witała, J. Golak, R. Skibiński, WN. Polyzou, C. Elster
abstract
The phase equivalent relativistic NN potential, which is related by a nonlinear equation to the original nonrelativistic potential, is used to construct the mass operator (rest Hamiltonian) of the 3-nucleon system. Employing the CD Bonn NN potential, the solution of the relativistic 3N Faddeev equation for 3 H shows slightly less binding energy than the corresponding nonrelativistic result. The effect of the Wigner spin rotation on the binding is very small.
RELATIVISTIC EFFECTS IN 3N REACTIONS
H. Witała, J. Golak, R. Skibiński, W. Glockle, WN. Polyzou, H. Kamada
abstract
We solved the three-nucleon Faddeev equation in a Poincare invariant model of the three-nucleon system. Two-body interactions are generated so that when they are added to the two-nucleon invariant mass operator (rest energy) the two-nucleon S matrix is identical to the non-relativistic S matrix with a CD Bonn interaction. Cluster properties of the three-nucleon S-matrix determine how these two-nucleon interactions are embedded in the three-nucleon mass operator. Differences in the predictions of the relativistic and corresponding non-relativistic models for elastic and breakup processes are investigated. Of special interest are the lowering of the A(y) maximum in elastic nucleon-deuteron (Nd) scattering below approximate to 25 MeV caused by the Wigner spin rotations and the significant changes of the breakup cross sections in certain regions of the phase-space.
Exact three-dimensional wave function and the on-shell t matrix for the sharply cut-off Coulomb potential: Failure of the standard renormalization factor
W. Glokle, J. Golak, R. Skibiński, H. Witała
abstract
The three-dimensional wave function for a sharply cut-off Coulomb potential is analytically derived. The asymptotic form of the related scattering amplitude reveals a failure of the standard renormalization factor which is believed to be generally valid for any type of screening.
THREE-NUCLEON INTERACTION DYNAMICS STUDIED VIA THE DEUTERON-PROTON BREAKUP
E. Stephan, S. Kistryn, N. Kalantar-Nayestanaki, A. Biegun, K. Bodek, I. Ciepal, A. Deltuva, E. Epelbaum, M. Eslami-Kalantari, AC. Fonseca, W. Glockle, J. Golak, V. Jha, H. Kamada, D. Kirillov, D. Kirillov, M. Kis, S. Kliczewski, B. Klos, A. Kozela, M. Kravcikova, VM. Kyryanchuk, M. Lesiak, H. Machner, A. Magiera, M. Mahjour-Shafiei, G. Martinska, J. Messchendorp, A. Micherdzinska, A. Nogga, N. Piskunov, D. Protic, A. Ramazani, P. Von Rossen, BJ. Roy, H. Sakai, PU. Sauer, K. Sekiguchi, I. Sitnik, R. Siudak, R. Skibinski, R. Sworst, J. Urban, H. Witala, J. Zejma, W. Zipper
abstract
A large set of high precision cross sections, vector A(x), A(y) and tensor A(xx), A(xy), A(yy) analyzing powers for the (1)H((d) over right arrow ,pp)n breakup reaction were measured at 130 MeV beam energy with the detection system covering a large part of the phase space. Results are compared with rigorous theoretical calculations employing various models of the three-nucleon system dynamics. The cross section data allowed to establish evidence for three-nucleon force contributions and to confirm predictions of sizable effect of the Coulomb force in the breakup reaction. Analyzing power data are generally quite well described by theoretical predictions even with pure NN interactions. However, in some regions discrepancies has been observed for tensor analyzing powers, only rarely cured by inclusion of the three nucleon force. This indicates incompletness of the present-day treatment of the spin part of three nucleon system dynamics.
THREE-NUCLEON INTERACTION DYNAMICS STUDIED VIA THE DEUTERON-PROTON BREAKUP
E. Stephan, S. Kistryn, N. Kalantar-Nayestanaki, A. Biegun, K. Bodek, I. Ciepal, A. Deltuva, E. Epelbaum, M. Eslami-Kalantari, AC. Fonseca, W. Glockle, J. Golak, V. Jha, H. Kamada, D. Kirillov, D. Kirillov, M. Kis, S. Kliczewski, B. Klos, A. Kozela, M. Kravcikova, VM. Kyryanchuk, M. Lesiak, H. Machner, A. Magiera, M. Mahjour-Shafiei, G. Martinska, J. Messchendorp, A. Micherdzinska, A. Nogga, N. Piskunov, D. Protic, A. Ramazani, P. Von Rossen, BJ. Roy, H. Sakai, PU. Sauer, K. Sekiguchi, I. Sitnik, R. Siudak, R. Skibiński, R. Sworst, J. Urban, H. Witała, J. Zejma, W. Zipper
abstract
A large set of high precision cross sections, vector A(x), A(y) and tensor A(xx), A(xy), A(yy) analyzing powers for the (1)H((d) over right arrow ,pp)n breakup reaction were measured at 130 MeV beam energy with the detection system covering a large part of the phase space. Results are compared with rigorous theoretical calculations employing various models of the three-nucleon system dynamics. The cross section data allowed to establish evidence for three-nucleon force contributions and to confirm predictions of sizable effect of the Coulomb force in the breakup reaction. Analyzing power data are generally quite well described by theoretical predictions even with pure NN interactions. However, in some regions discrepancies has been observed for tensor analyzing powers, only rarely cured by inclusion of the three nucleon force. This indicates incompletness of the present-day treatment of the spin part of three nucleon system dynamics.
Four-nucleon force contribution to the binding energy of He-4
A. Nogga, D. Rozpedzik, E. Epelbaum, W. Glockle, J. Golak, H. Kamada, R. Skibiński, H. Witała
abstract
We study the four-nucleon force contribution to the binding energy of He-4 in the framework of chiral nuclear interactions. The four-nucleon forces start to contribute in the next-to-next-to-next-to leading order. We discuss our power counting expectations for the size of the 4N contribution and then explicitly calculate it in first order perturbation theory. Our expectations agree with the results. Quantitatively, the contribution might be significant. This motivates further studies in more complex nuclei.
The proton-proton scattering without Coulomb force renormalization
R. Skibiński, J. Golak, H. Witała, W. Glockle
abstract
We demonstrate numerically that proton-proton (pp) scattering observables can be determined directly by standard short range methods using a screened pp Coulomb force without renormalization. We numerically investigate solutions of the 3-dimensional Lippmann-Schwinger (LS) equation for an exponentially screened Coulomb potential. For the limit of large screening radii we confirm analytically predicted properties for off-shell, half-shell and on-shell elements of the Coulomb t-matrix.
A novel treatment of the proton-proton Coulomb force in proton-deuteron Faddeev calculations
H. Witała, J. Golak, R. Skibiński, W. Glockle
abstract
We present resently introduced novel approach to include the proton-proton (pp) Coulomb force into the momentum space three-nucleon (3N) Faddeev calculations. It is based on a standard formulation for short range forces and relies on a screening of the long-range Coulomb interaction. In order to avoid all uncertainties connected with an application of the partial wave expansion, unsuitable when working with long-range forces, we apply directly the 3-dimensional pp screened Coulomb t-matrix. That main new ingredient, the 3-dimensional screened pp Coulomb t-matrix, is obtained by a numerical solution of the 3-dimensional Lippmann-Schwinger (LS) equation. Using a simple dynamical model for the nuclear part of the interaction we demonstrate the feasibility of that approach. The physical elastic pd scattering amplitude has a well defined screening limit and does not require renormalisation. Well converged elastic pd cross sections are obtained at finite screening radii. Also the proton-deuteron (pd) breakup observables can be determined from the resulting on-shell 3N amplitudes increasing the screening radius. However, contrary to the pd elastic scattering, the screening limit exists only after renormalisation of the pp t-matrices.
Treatment of Two Nucleons in Three Dimensions
I. Fachruddin, C. Elster, J. Golak, R. Skibiński, W. Glockle, H. Witała
abstract
We extend a new treatment proposed for two-nucleon (2N) and three-nucleon (3N) bound states to 2N scattering. This technique takes momentum vectors as variables, thus, avoiding partial wave decomposition, and handles spin operators analytically. We apply the general operator structure of a nucleon-nucleon (NN) potential to the NN T-matrix, which becomes a sum of six terms, each term being scalar products of spin operators and momentum vectors multiplied with scalar functions of vector momenta. Inserting this expansions of the NN force and T-matrix into the Lippmann-Schwinger equation allows to remove the spin dependence by taking traces and yields a set of six coupled equations for the scalar functions found in the expansion of the T-matrix.
Approximate Three-Dimensional Wave Function and the T-Matrix for the Sharply Cut Off Coulomb Potential
J. Golak, W. Glockle, R. Skibiński, H. Witała
abstract
For a sharply cut-off Coulomb potential we derive analytically the asymptotic form of the three-dimensional wave function and the related scattering amplitude. We show a failure of the standard renormalization factor which is believed to be generally valid for any type of screening. We obtain also the asymptotic form of the corresponding three-dimensional half-shell t-matrix. Our results are fully supported by the numerical solutions of the three-dimensional Lippmann-Schwinger equation.
Calculations of the Triton Binding Energy with a Lorentz Boosted Nucleon-Nucleon Potential
H. Kamada, W. Glockle, H. Witała, J. Golak, R. Skibiński, WN. Polyzou, C. Elster
abstract
We study the binding energy of the three-nucleon system in relativistic models that use two different relativistic treatments of the potential that are phase equivalent to realistic NN interactions. One is based on a unitary scale transformation that relates the non-relativistic center-of-mass Hamiltonian to the relativistic mass (rest energy) operator and the other uses a non-linear equation that relates the interaction in the relativistic mass operator to the non-relativistic interaction. In both cases Lorentz-boosted interactions are used in the relativistic Faddeev equation to solve for the three-nucleon binding energy. Using the same realistic NN potentials as input, the solution of the relativistic three-nucleon Faddeev equation for H-3 shows slightly less binding energy than the corresponding nonrelativistic result. The effect of the Wigner spin rotation on the binding is very small.
Relativistic effects in the 3N continuum and the A (y) puzzle
H. Witała, J. Golak, R. Skibiński, H. Kamada, W. Glockle, WN. Polyzou
abstract
The three-nucleon (3N) Faddeev equation is solved in a Poincar,-invariant model of the three-nucleon system. Two-body interactions are generated so that when they are added to the two-nucleon invariant mass operator (rest energy) the two-nucleon S-matrix is identical to the non-relativistic S-matrix with a CD Bonn interaction. Cluster properties of the three-nucleon S-matrix determine how these two-nucleon interactions are embedded in the three-nucleon mass operator. Differences in the predictions of the relativistic and corresponding non-relativistic models for elastic and breakup processes are investigated. Of special interest are the lowering of the A (y) maximum in elastic nucleon-deuteron (Nd) scattering below a parts per thousand 25 MeV caused by the Wigner spin rotations and the significant changes of the breakup cross sections in certain regions of the phase space.
Studies of the three-nucleon system dynamics: Cross sections of the deuteron-proton breakup at 130 MeV
S. Kistryn, E. Stephan, N. Kalantar-Nayestanaki, A. Biegun, K. Bodek, I. Ciepal, A. Deltuva, E. Epelbaum, AC. Fonseca, W. Glockle, J. Golak, H. Kamada, M. Kis, B. Klos, A. Kozela, A. Nogga, M. Mahjour-Shafiei, A. Micherdzinska, PU. Sauer, R. Skibiński, R. Sworst, H. Witała, J. Zejma, W. Zipper
abstract
The three-nucleon system is the simplest non-trivial testing ground in which the quality of modern nucleon-nucleon interaction models, as well as additional dynamical ingredients referred to as three-nucleon forces, can be probed quantitatively by means of a rigorous technique of solving the Faddeev equations. A large set of high precision, exclusive cross-section data for the (1)H((d) over right arrow, pp)n breakup reaction at 130 MeV was obtained at KVI, Groningen. It allowed to establish for the first time a clear evidence of the three-nucleon force contributions to the cross sections of the breakup process and to confirm recent predictions of sizable influences of the Coulomb force in this reaction.
Relativity in the three-nucleon system
H. Kamada, W. Gloeckle, H. Witała, J. Golak, R. Skibiński, WN. Polyzou
abstract
A Poincar,-invariant formulation of the three-body system is used. The two-body force embedded in the three-particle Hilbert space is generated out of the high-precision NN forces by solving a nonlinear equation. The solution of the relativistic 3N Faddeev equation for (3)H reveals less binding energy than for the nonrelativistic one. The effect of the Wigner spin rotation on the binding energy is very small.
Relativity and the low-energy nd A(y) puzzle
H. Witała, J. Golak, R. Skibiński, W. Glockle, WN. Polyzou, H. Kamada
abstract
We solve the Faddeev equation in an exactly Poincare invariant formulation of the three-nucleon problem. The dynamical input is a relativistic nucleon-nucleon (NN) interaction that is exactly on-shell equivalent to the high-precision CD Bonn NN interaction. S-matrix cluster properties dictate how the two-body dynamics is embedded in the three-nucleon mass operator (rest Hamiltonian). We find that for neutron laboratory energies above approximate to 20 MeV relativistic effects on Ay are negligible. For energies below approximate to 20 MeV dynamical effects lower the nucleon analyzing power maximum slightly by approximate to 2% and Wigner rotations lower it further up to approximate to 10%, thereby increasing disagreement between data and theory. This indicates that three-nucleon forces (3NF) must provide an even larger increase of the Ay maximum than expected up to now.
Influence of three-nucleon force effects on polarization observables of the H-1((d)over-bar,pp)n breakup reaction at 130 mev
R. Sworst, S. Kistryn, E. Stephan, A. Biegun, K. Bodek, I. Ciepal, E. Epelbaum, W. Gloeckle, J. Golak, N. Kalantar-Nayastenaki, H. Kamada, B. Klos, A. Kozela, A. Nogga, R. Skibiński, H. Witała, J. Zejma, W. Zipper
abstract
High-precision vector and tensor breakup analyzing powers for the reaction H-1((d) over bar ,pp)n at 130 MeV were evaluated for a large phase space region. Results are compared with rigorous theoretical calculations based on realistic nucleon-nucleon potentials as well as on chiral perturbation theory approach. Theoretical predictions generally describe data quite well, only in a few cases influence of three-nucleon forces is significant.
Vector and tensor analyzing powers of elastic deuteron-proton scattering at 130 MeV deuteron beam energy
E. Stephan, S. Kistryn, R. Sworst, A. Biegun, K. Bodek, I. Ciepal, A. Deltuva, E. Epelbaum, A. Fonseca, W. Glockle, J. Golak, N. Kalantar-Nayestanaki, H. Kamada, M. Kis, A. Kozela, M. Mahjour-Shafiei, A. Micherdzinska, A. Nogga, PU. Sauer, R. Skibiński, H. Witała, J. Zejma, W. Zipper
abstract
High precision vector and tensor analyzing power data of the deuteron-proton elastic scattering at 130 MeV deuteron beam energy have been measured in a large range of angles. They are compared with theoretical predictions obtained in various approaches: with realistic potentials for pure NN interactions, with the inclusion of a three-nucleon force, and in the framework of chiral perturbation theory. All the theoretical calculations describe roughly the main features of the measured distributions, but none of them can reproduce all their details. This indicates the need for further development of the three-nucleon force models.
Differential cross section and analyzing power measurements for (n)over-right-arrowd elastic scattering at 248 MeV
Y. Maeda, H. Sakai, K. Fujita, MB. Greenfield, K. Hatanaka, M. Hatano, J. Kamiya, T. Kawabata, H. Kuboki, H. Okamura, J. Rapaport, T. Saito, Y. Sakemi, M. Sasano, K. Sekiguchi, Y. Shimizu, K. Suda, Y. Tameshige, A. Tamii, T. Wakasa, K. Yako, J. Blomgren, P. Mermod, AR. Ohrn, MR. Osterlund, H. Witała, A. Deltuva, AC. Fonseca, PU. Sauer, W. Glockle, J. Golak, H. Kamada, A. Nogga, R. Skibiński
abstract
The differential cross sections and vector analyzing powers for nd elastic scattering at E-n=248 MeV were measured for 10 degrees-180 degrees in the center-of-mass (c.m.) system. To cover the wide angular range, the experiments were performed separately by using two different setups for forward and backward angles. The data are compared with theoretical results based on Faddeev calculations with realistic nucleon-nucleon (NN) forces such as AV18, CD Bonn, and Nijmegen I and II, and their combinations with the three-nucleon forces (3NFs), such as Tucson-Melbourne 99 (TM99), Urbana IX, and the coupled-channel potential with Delta-isobar excitation. Large discrepancies are found between the experimental cross sections and theory with only 2N forces for theta(c.m.)>90 degrees. The inclusion of 3NFs brings the theoretical cross sections closer to the data but only partially explains this discrepancy. For the analyzing power, no significant improvement is found when 3NFs are included. Relativistic corrections are shown to be small for both the cross sections and the analyzing powers at this energy. For the cross sections, these effects are mostly seen in the very backward angles. Compared with the pd cross section data, quite significant differences are observed at all scattering angles that cannot be explained only by the Coulomb interaction, which is usually significant at small angles.
Lorentz boosted nucleon-nucleon potential applied to the (3)(H)over-right-arrowe((e)over-right-arrow e'p)pn and (3)(H)over-right-arrowe((e)over-right-arrow, e'n)pp reactions
J. Golak, R. Skibiński, H. Witała, W. Glockle, A. Nogga, H. Kamada
abstract
We formulate an approximate relativistic framework for an analysis of the 3He(e, e'p)pn and 3He(e, en)pp reactions. Restricting the rescattering series to one term linear in the two-nucleon (2N) t-matrix we incorporate various relativistic features when calculating a nuclear current matrix element. These relativistic ingredients encompass the relativistic 3 He wave function based on the concept of the Lorentz boosted nucleon-nucleon potential together with the boosted 2N t-matrix, relativistic kinematics and relativistic single-nucleon current operator. This allows us to estimate the magnitude of certain relativistic effects not included in the standard nonrelativistic approach. A more complete inclusion of relativity would require that the current operator obeys the covariance equations and the final three-nucleon (3N) scattering state with complete final state interactions (FSI) should be properly boosted. We provide some discussion on those issues.
Cross sections of the deuteron-proton breakup as a probe of three-nucleon system dynamics
S. Kistryn, E. Stephan, N. Kalantar-Nayestanaki, A. Biegun, B. Klos, Z. Sworst, K. Bodek, I. Ciepal, A. Deltuva, E. Epelbaum, AC. Fonseca, W. Gloeckle, J. Golak, H. Kamada, M. Ki, A. Kozela, M. Mahjour-Shafiei, A. Micherdzinska, A. Nogga, PU. Sauer, R. Skibiński, H. Witała, J. Zejma, W. Zipper
abstract
The three-nucleon system is the simplest, non-trivial testing ground which allows one to probe quantitatively modern nucleon-nucleon interaction models. The rigorous technique of solving the Faddeev equations for the three-nucleon system allows one to test the influence of additional dynamical ingredients, referred to as three-nucleon forces, as well as the Coulomb interaction and relativistic effects. A large set of high precision, exclusive cross-section data for the H-1(d,pp)n breakup reaction at 130 MeV was obtained at KVI, Groningen. This allowed us to establish for the first time clear evidence for three-nucleon force contributions to the cross sections of the breakup process and to confirm recent predictions of a sizable influence of the Coulomb force in this reaction.
Relativistic effects in neutron-deuteron elastic scattering
H. Witała, J. Golak, W. Glokle, H. Kamada
abstract
We solved the three-nucleon (3N) Faddeev equation including relativistic features at lab incoming neutron lab energies E-n(lab)=28, 65, 135 and 250 MeV. Those features are relativistic kinematics, boost effects and Wigner spin rotations. As dynamical input a relativistic nucleon-nucleon (NN) interaction exactly on-shell equivalent to the AV18 NN potential has been used. The boost effects are significant at higher energies. The effects of Wigner rotations for elastic scattering observables were found to be small. There are rather small effects in the cross section, which are mostly restricted to the backward angles.
Three-nucleon force effects in 3N hadronic and photonic reactions
H. Witała, R. Skibiński, J. Golak, W. Glockle, R. Kamada, A. Nogga, WN. Polyzou
abstract
Results on three-nucleon (3N) elastic scattering and breakup below the pion production threshold are discussed with emphasis on the need for a three-nucleon force (3NF). The large discrepancies found between a theory based on numerical solutions of 3N Faddeev equations with modem NN potentials only and data point to the need for 3NF's. Successes and failures of the present 3NF models, mostly of a 2 pi-exchange nature, to describe high precision 3N data are discussed. Effects due to relativity both in elastic nucleon-deuteron (Nd) scattering and breakup reaction are presented and consequences for a 3NF study pointed out. As an application of 3N bound and scattering states, results for photodisintegration of 3N bound states are shown.
A large, precise set of polarization observables for deuteron-proton breakup at 130 MeV
E. Stephan, S. Kistryn, N. Kalantar-Nayestanaki, A. Biegun, K. Bodek, I. Ciepal, A. Deltuva, E. Epelbaun, AC. Fonseca, W. Gloeckle, J. Golak, H. Kamada, M. Kis, B. Klos, A. Kozela, M. Malljour-Shafiei, A. Micherdzinska, A. Nogga, PU. Sauer, R. Skibiński, R. Sworst, H. Witała, J. Zejma, W. Zipper
abstract
High precision vector A(x), A(y) and tensor A(xx), A(xy), A(yy) analyzing powers for the H-1((d) over right arrow, pp)n breakup reaction were measured at 130 MeV beam energy with the detection system covering a large part of the phase space. Results are compared with rigorous theoretical calculations based on realistic nucleon-nucleon potentials, also with a so-called three-nucleon force included, as well as on chiral perturbation theory. Theoretical predictions generally describe the data quite well, but in some regions discrepancies have been observed, which indicate incompleteness of the present-day treatment of three nucleon dynamics.
Partial wave decomposition of 2 pi-1 pi exchange three-nucleon force in chiral effective field theory
H. Kamada, E. Epelbaum, A. Nogga, UG. Meissner, H. Witała, J. Golak, R. Skibiński, W. Gloeckle
abstract
The 3-nucleon force at (NLO)-L-3 in chiral effective field theory is briefly reviewed. The two-pion-one-pion-exchange 3-nucleon force is decomposed into partial waves.
Relativistic effects in exclusive neutron-deuteron breakup
R. Skibiński, H. Witała, J. Golak
abstract
We extended the study of relativistic effects in neutron-deuteron scattering to the exclusive breakup. To this aim we solved the three-nucleon Faddeev equation including such relativistic features as relativistic kinematics and boost effects at incoming neutron laboratory energies E-n(lab) = 65 MeV, 156 MeV and 200MeV. As dynamical input a relativistic nucleon-nucleon interaction exactly on-shell equivalent to the CD Bonn potential has been used. We found that the magnitude of relativistic effects increases with the incoming neutron energy and, depending on the phase-space region, relativity can increase as well as decrease the nonrelativistic breakup cross-section. In some regions of the breakup phase-space dynamical boost effects are important. For a number of measured exclusive cross-sections relativity seems to improve the description of data.
A first estimation of chiral four-nucleon force effects in He-4
D. Rozpedzik, J. Golak, R. Skibiński, H. Witała, W. Glockle, E. Epelbaum, A. Nogga, H. Kamada
abstract
We estimate four-nucleon force effects between different He-4 wave functions by calculating the expectation values of four-nucleon potentials which were recently derived within the framework of chiral effective field theory. We find that the four-nucleon force is attractive for the wave functions with a totally symmetric momentum part. The additional binding energy provided by the long-ranged part of the four-nucleon force is of the order of a few hundred keV.
Nucleon-deuteron capture with chiral potentials
R. Skibiński, J. Golak, H. Witała, W. Glockle, A. Nogga, E. Epelbaum
abstract
Present day chiral nucleon-nucleon potentials up to next-to-next-to-next-to leading order and three nucleon forces at next-to-next-to leading order are used to analyze nucleon-deuteron radiative capture at deuteron laboratory energies below E-d approximate to 100 MeV. The differential cross section and the deuteron analyzing powers A(y)(d) and A(yy) are presented and compared to data. The theoretical predictions are obtained in the momentum-space Faddeev approach using the nuclear electromagnetic current operator with exchange currents introduced via the Siegert theorem. The chiral forces provide the same quality of data description as a combination of the two-nucleon AV18 and the three-nucleon Urbana IX interactions. However, the different parametrizations of the chiral potentials lead to broad bands of predictions.
The elastic pd scattering analyzing powers and spin correlation coefficients at E-p(lab)=135 and 200 MeV: Three-nucleon force and relativistic effects
H. Witała, R. Skibiński, J. Golak, W. Glockle, A. Nogga, H. Kamada
abstract
The rich set of data for analyzing powers and spin correlation coefficients in pd elastic scattering at E-p(lab) = 135 and 200 MeV taken at IUCF has been compared to theoretical predictions based on modern nuclear forces. To this aim the three-nucleon Faddeev equations have been solved with standard nucleon-nucleon potentials (AV18, CD Bonn, NijmI and II) alone or combined with the 2 pi-exchange Tucson-Melbourne three-nucleon force. For the AV18 potential also the Urbana IX three-nucleon interaction has been used. For some spin observables the addition of these three-nucleon forces improves the description of data whereas in other cases the description deteriorates. The relativistic effects for all studied spin observables have been investigated and found to be small. The conclusion is that significant parts of the three-nucleon force are missing.
Measurement of the H-2(n,gamma)H-3 reaction cross section between 10 and 550 keV
Y. Nagai, T. Kobayashi, T. Shima, T. Kikuchi, K. Takaoka, M. Igashira, J. Golak, R. Skibiński, H. Witała, A. Nogga, W. Glockle, H. Kamada
abstract
We have measured for the first time the cross section of the H-2(n,gamma)H-3 reaction at an energy relevant to big-bang nucleosynthesis by employing a prompt discrete gamma-ray detection method. The outgoing photons have been detected by means of anti-Compton NaI(Tl) spectrometers with a large signal-to-noise ratio. The resulting cross sections are 2.23 +/- 0.34,1.99 +/- 0.25, and 3.76 +/- 0.41 mu b at E-n=30.5,54.2, and 531 keV, respectively. At E-n=30.5 keV the cross section differs from the value reported previously by a factor of 2. Based on the present data the reaction rate has been obtained for temperatures in the range 10(7)-10(10) K. The astrophysical impact of the present result is discussed. The obtained cross sections are compared with a theoretical calculation based on the Faddeev approach, which includes meson exchange currents as well as a three-nucleon force.
Cross sections and tensor analyzing powers A(yy) of the reaction H-1((d)over-right-arrow, pp)n in "symmetric constant relative energy" geometries at E-d=19 MeV
J. Ley, C. Duweke, R. Emmerich, A. Imig, HPG. Schieck, J. Golak, H. Witała, E. Epelbaum, A. Deltuva, AC. Fonseca, W. Glockle, UG. Meissner
abstract
We measured the cross sections and tensor analyzing powers of the H-1(d,pp)n breakup reaction at E-d=19 MeV in four symmetric constant relative energy (SCRE) configurations. The data are compared with theoretical predictions from four different approaches: the first based on high-precision (semi)phenomenological potentials alone or, the second, combined with model three-nucleon forces, and the third based on chiral forces up to next-to-next-to-leading order (NNLO) in the chiral expansion. In these cases the Coulomb interaction is not included. In addition, a fourth approach consists in a comparison with predictions based on CD Bonn including the Delta excitation and the Coulomb force. In all cases the measured cross sections are significantly below the theoretical values, whereas the magnitudes of the tensor analyzing powers agree within the error bars in three of the four cases. The apparent discrepancies in the breakup cross sections are similar to the known differences for the space-star breakup. This adds to the data base of unsolved low-energy discrepancies (puzzles).
Testing nuclear forces by polarization transfer coefficients in d((p)over-right-arrow,(p)over-right-arrow)d and d((p)over-right-arrow,(d)over-right-arrow)p reactions at E-p(lab)=22.7 MeV
H. Witała, J. Golak, R. Skibiński, W. Glockle, A. Nogga, E. Epelbaum, H. Kamada, A. Kievsky, M. Viviani
abstract
The proton to proton polarization transfer coefficients K-x(x'),K-y(y'), and K-z(x'), and the proton to deuteron polarization transfer coefficients K-x(x'),K-y(y'),K-z(x'), K(x)(y')z('),K(y)(z')z('),K(z)(y')z('),K(y)(x')z('), and K(y)(x')x(')-y(')y(') were measured in d(p,p)d and d(p,d)p reactions, respectively, at E-p(lab)=22.7 MeV. The data were compared to predictions of modern nuclear forces obtained by solving the three-nucleon Faddeev equations in momentum space. Realistic (semi)phenomenological nucleon-nucleon potentials combined with model three-nucleon forces and modern chiral nuclear forces were used. The AV18, CD Bonn, and Nijm I and II nucleon-nucleon interactions were applied alone or combined with the Tucson-Melbourne 99 three-nucleon force, adjusted separately for each potential to reproduce the triton binding energy. For the AV18 potential, the Urbana IX three-nucleon force was also used. In addition, chiral NN potentials in the next-to-leading order and chiral two- and three-nucleon forces in the next-to-next-to-leading order were applied. Only when three-nucleon forces are included does a satisfactory description of all data result. For the chiral approach, the restriction to the forces in the next-to-leading order is insufficient. Only when going over to the next-to-next-to-leading order does one get a satisfactory description of the data, similar to the one obtained with the (semi)phenomenological forces.
Selectivity of the nucleon-induced deuteron breakup and relativistic effects
H. Witała, J. Golak, R. Skibiński
abstract
Theoretical predictions for the nucleon-induced deuteron breakup process based on solutions of the three-nucleon Faddeev equation including such relativistic features as the relativistic kinematics and boost effects are presented. Large changes of the breakup cross section in some complete configurations are found at higher energies. The predicted relativistic effects, which are mostly of dynamical origin, seem to be supported by existing data. (c) 2006 Elsevier B.V. All rights reserved.
New data for total He-3(gamma,p)D and He-3(gamma,pp)n cross sections compared to current theory
S. Naito, Y. Nagai, T. Shima, H. Makii, K. Mishima, K. Tamura, H. Toyokawa, H. Ohgaki, J. Golak, R. Skibiński, H. Witała, W. Glockle, A. Nogga, H. Kamada
abstract
A simultaneous measurement of the cross sections of the He-3(gamma, p) D and He-3(gamma, pp) n reactions has been performed for the first time using monoenergetic pulsed gamma-rays at < E gamma > = 10.2 and 16.0 MeV. Charged fragments from the reactions were detected with an efficiency of 100% using a 4 pi time projection chamber containing 3He gas as an active target. The incident gamma-ray flux was measured by a gamma-ray detector. Both the track and energy loss signals of charged fragments were obtained in an off-line analysis and used to clearly identify the reaction channel. Thus, the (gamma, p) and (gamma, pp) cross sections have been determined with small uncertainty. A comparison of the new data to current theory based on the AV18+Urbana IX nuclear forces including pi- and p-like meson exchange currents shows a severe discrepancy at 10.2 MeV, while at 16.0 MeV data and theory agree within about 12%. Three-nucleon force effects are small, but in general shift the theory in the correct direction.
Three-nucleon force effects in the analyzing powers of the (d)over-right-arrowp breakup at 130 MeV
A. Biegun, E. Stephan, S. Kistryn, K. Bodek, I. Ciepal, A. Deltuva, E. Epelbaum, W. Glockle, J. Golak, N. Kalantar-Nayestanaki, H. Kamada, M. Kis, B. Klos, A. Kozela, J. Kuros-Zolnierczuk, M. Mahjour-Shafiei, UG. Meissner, A. Micherdzinska, A. Nogga, PU. Sauer, R. Skibiński, R. Sworst, H. Witała, J. Zejma, W. Zipper
abstract
A measurement of the analyzing powers for the H-1((d) over right arrow pp)n breakup reaction at 130 MeV polarized deuteron beam energy was carried out at KVI Groningen. The experimental setup covered a large fraction of the phase space. Obtained tensor analyzing powers T-22 for selected kinematical configurations have been compared to theoretical predictions based on various approaches: the rigorous Faddeev calculations using the realistic nucleon-nucleon potentials with and without three nucleon force (3NF) models, predictions of the chiral perturbation theory, and coupled channel calculations with the explicit Delta degrees of freedom. In the presented configurations the results of all predictions are very close to one another and there are no significant 3NF influences. Not all of the data can be satisfactory reproduced by the theoretical calculations.
Proton polarizations in polarized He-3 studied with the He-3(->)(e(->),e ' p)d and He-3(->)(e(->),e ' p)pn processes
J. Golak, R. Skibiński, H. Witała, W. Glockle, A. Nogga, H. Kamada
abstract
We study within the Faddeev framework the He-3(->)(e(->),e(')p)d as well as the He-3(->)(e(->),e(')p)pn and He-3(->)(e(->),e(')n)pp reactions in order to extract information on the proton and neutron polarization in polarized He-3. We achieve clear analytical insight for simplified dynamical assumptions and define conditions for experimental access to important He-3 properties. In addition we point to the possibility of measuring the electromagnetic proton form factors in the process He-3(->)(e(->),e(')p)d which would test the dynamical picture and put limits on medium corrections of the form factors.
Resolving the discrepancy of 135 MeV pd elastic scattering cross sections and relativistic effects
K. Sekiguchi, H. Sakai, H. Witała, W. Glockle, J. Golak, K. Hatanaka, M. Hatano, K. Itoh, H. Kamada, H. Kuboki, Y. Maeda, A. Nogga, H. Okamura, T. Saito, N. Sakamoto, Y. Sakemi, M. Sasano, Y. Shimizu, K. Suda, A. Tamii, T. Uesaka, T. Wakasa, K. Yako
abstract
Three precise measurements for elastic pd scattering at 135 MeV/A have been performed with the three different experimental setups. The cross sections are described well by the theoretical predictions based on modern nucleon-nucleon forces combined with three-nucleon forces. Relativistic Faddeev calculations show that relativistic effects are restricted to backward angles. This result supports the two measurements recently reported by RIKEN and contradicts the KVI data.
Polarization observables in the semiexclusive photoinduced three-body breakup of He-3
R. Skibiński, J. Golak, H. Witała, W. Glockle, A. Nogga, H. Kamada
abstract
The photon and He-3 analyzing powers as well as spin correlation coefficients in the semiexclusive three-body photodisintegration of He-3 are investigated for incoming photon laboratory energies E-gamma=12,40, and 120 MeV. The nuclear states are obtained by solving three-body Faddeev equations with the AV18 nucleon-nucleon potential alone or supplemented with the UrbanaIX three-nucleon force. Explicit pi- and rho-meson exchange currents are taken into account, but we also compare to other models of the electromagnetic current. In some kinematical conditions we have found strong effects of the three-nucleon force for the He-3 analyzing power and spin correlation coefficients, as well strong sensitivities to the choice of the currents. This set of predictions should be a useful guidance for the planning of measurements. In addition, we compare our results for two-body He-3 breakup induced by polarized photons with a few existing data.
Systematic study of three-nucleon force effects in the cross section of the deuteron-proton breakup at 130 MeV
S. Kistryn, E. Stephan, A. Biegun, K. Bodek, A. Deltuva, E. Epelbaum, K. Ermisch, W. Glockle, J. Golak, N. Kalantar-Nayestanaki, H. Kamada, M. Kis, B. Klos, A. Kozela, J. Kuros-Zolnierczuk, M. Mahjour-Shafiei, UG. Meissner, A. Micherdzinska, A. Nogga, PU. Sauer, R. Skibiński, R. Sworst, H. Witała, J. Zejma, W. Zipper
abstract
High-precision cross-section data of the deuteron-proton breakup reaction at 130 MeV are presented for 72 kinematically complete configurations. The data cover a large region of the available phase space, divided into a systematic grid of kinematical variables. They are compared with theoretical predictions, in which the full dynamics of the three-nucleon (3N) system is obtained in three different ways: realistic nucleon-nucleon (NN) potentials are combined with model 3N forces (3NF's) or with an effective 3NF resulting from explicit treatment of the Delta-isobar excitation. Alternatively, the chiral perturbation theory approach is used at the next-to-next-to-leading order with all relevant NN and 3N contributions taken into account. The generated dynamics is then applied to calculate cross-section values by rigorous solution of the 3N Faddeev equations. The comparison of the calculated cross sections with the experimental data shows a clear preference for the predictions in which the 3NF's are included. The majority of the experimental data points are well reproduced by the theoretical predictions. The remaining discrepancies are investigated by inspecting cross sections integrated over certain kinematical variables. The procedure of global comparisons leads to establishing regularities in disagreements between the experimental data and the theoretically predicted values of the cross sections. They indicate deficiencies still present in the assumed models of the 3N system dynamics.
Measurement of the asymmetries in (3)(H)over-right-arrowe((e)over-right-arrow, e ' p)d and (3)(H)over-right-arrowe((e)over-right-arrow, e'p)np
P. Achenbach, A. Baumann, R. Bohm, B. Boillat, D. Bosnar, C. Carasco, M. Ding, MO. Distler, J. Friedrich, W. Glockle, J. Golak, Y. Goussev, P. Grabmayr, W. Heil, A. Hugli, P. Jennewein, GJ. Manas, J. Jourdan, H. Kamada, T. Klechneva, B. Krusche, KW. Krygier, JG. Llongo, M. Lloyd, M. Makek, H. Merkel, C. Micheli, U. Muller, A. Nogga, R. Neuhausen, C. Normand, L. Nungesser, A. Ott, E. Otten, F. Parpan, RP. Benito, M. Potokar, D. Rohe, D. Rudersdorf, J. Schmiedeskamp, M. Seimetz, I. Sick, S. Sirca, R. Skibiński, S. Stave, G. Testa, R. Trojer, T. Walcher, M. Weis, H. Witała, H. Wohrle
abstract
The electron target asymmetrics A(parallel to) and A(perpendicular to) with target spin parallel and perpendicular to the momentum transfer q were measured for both the two- and three-body breakup of (3)He in the (3)He(e,e'p)- reaction. Polarized electrons were scattered off polarized (3)He in the quasielastic regime in parallel kinematics with the scattered electron and the knocked-out proton detected using the Three-Spectrometer Facility at MAMI The results are compared to Faddeev calculations which take into account Final-State Interactions as well as Meson Exchange Currents. The experiment confirms the prediction of a, large effect of Final-State Interactions in the asymmetry of the three-body breakup and of an almost negligible one for the two-body breakup.
Electron and photon scattering on three-nucleon bound states
J. Golak, R. Skibiński, H. Witała, W. Glockle, A. Nogga, H. Kamada
abstract
A big spectrum of processes induced by real and virtual photons on the He-3 and H-3 nuclei is theoretically investigated through many examples based on nonrelativistic Faddeev calculations for bound and continuum states. The modem nucleon-nucleon potential AV18 together with the three-nucleon force UrbanaIX is used. The single nucleon current is augmented by explicit pi- and rho-like two-body currents which fulfill the current continuity equation together with the corresponding parts of the AV 18 potential. We also employ the Siegert theorem, which induces many-body contributions to the current operator. The interplay of these different dynamical ingredients in the various electromagnetic processes is studied and the theory is compared to the experimental data. Overall we find fair to good agreement but also cases of strong disagreement between theory and experiment, which calls for improved dynamics. In several cases we refer the reader to the work of other groups and compare their results with ours. In addition we list a number of predictions for observables in different processes which would challenge this dynamical scenario even more stringently and systematically. (c) 2005 Elsevier B.V. All rights reserved.
Spin observables in deuteron-proton radiative capture at intermediate energies
AA. Mehmandoost-Khajeh-Dad, HR. Amir-Ahmadi, JCS. Bacelar, AM. van den Berg, R. Castelijns, A. Deltuva, ED. van Garderen, W. Glockle, J. Golak, N. Kalantar-Nayestanaki, H. Kamada, M. Kis, R. Koohi-Fayegh-Dehkordi, H. Lohner, M. Mahjour-Shafiei, H. Mardanpour, JG. Messchendorp, A. Nogga, P. Sauer, SV. Shende, R. Skibiński, H. Witała, HJ. Wortche
abstract
A radiative deuteron-proton capture experiment was carried out at KVI using polarized-deuteron beams at incident energies of 55, 66.5, and 90 MeV/nucleon. Vector and tensor-analyzing powers were obtained for a large angular range. The results are interpreted with the help of Faddeev calculations, which are based on modem two- and three-nucleon potentials. Our data are described well by the calculations, and disagree significantly with the observed tensor anomaly at RCNP. (c) 2005 Elsevier B.V. All rights reserved.
Systematic investigation of three-nucleon force effects in elastic scattering of polarized protons from deuterons at intermediate energies
K. Ermisch, HR. Amir-Ahmadi, AM. van den Berg, R. Castelijns, B. Davids, A. Deltuva, E. Epelbaum, W. Glockle, J. Golak, MN. Harakeh, M. Hunyadi, MA. de Huu, N. Kalantar-Nayestanaki, H. Kamada, M. Kis, M. Mahjour-Shafiei, A. Nogga, PU. Sauer, R. Skibiński, H. Witała, HJ. Wortche
abstract
The question, whether the high-quality nucleon-nucleon potentials can successfully describe the three-nucleon system, and to what extent three-nucleon forces (3NFs) play a role, has become very important in nuclear few-body physics. One kinematic region where effects because of 3NFs show up is in the minimum of the differential cross section of elastic nucleon-deuteron scattering. Another observable, which could give an indication about the contribution of the spin to 3NFs, is the vector analyzing power. To investigate the importance of 3NFs systematically over a broad range of intermediate energies, both observables of elastic proton-deuteron scattering have been measured at proton bombarding energies of 108, 120, 135, 150, 170, and 190 MeV, covering an angular range in the center-of-mass system between 30(degrees) and 170(degrees). The results show unambiguously the shortcomings of calculations employing only two-body forces and the necessity of the inclusion of 3NFs. They also show the limitations of the results of the present day models for few-nucleon systems at backward angles, especially at higher beam energies. New calculations based on chiral perturbation theory are also presented and compared with the data at the lowest energy.
Relativistic effects in neutron-deuteron elastic scattering
H. Witała, J. Golak, W. Glockle, H. Kamada
abstract
We solved the three-nucleon (3N) Faddeev equation including relativistic features at incoming neutron lab energies E-n(lab) = 28,65,135, and 250 MeV. Those features are relativistic kinematics, boost effects and Wigner spin rotations. As dynamical input a relativistic nucleon-nucleon (NN) interaction exactly on-shell equivalent to the AV18 NN potential has been used. The effects of Wigner rotations for elastic scattering observables were found to be small. The boost effects are significant at higher energies. They diminish the transition matrix elements at higher energies and lead in spite of the increased relativistic phase-space factor as compared to the nonrelativistic one to rather small effects in the cross section, which are mostly restricted to the backward angles.
The reaction H-2(p,pp)n in three kinematical configurations at E-p=16 MeV
C. Duweke, R. Emmerich, A. Imig, J. Ley, G. Tenckhoff, HP. Schieck, J. Golak, H. Witała, E. Epelbaum, W. Glockle, A. Nogga
abstract
We measured the cross sections of the H-2(p,pp)n breakup reaction at E-p=16 MeV in three kinematical configurations: the np final-state interaction (FSI), the coplanar star (CST), and an intermediate-star (IST) geometry. The cross sections are compared with theoretical predictions based on the CD Bonn potential alone and combined with the updated 2 pi-exchange Tucson-Melbourne three-nucleon force (TM99'), calculated without inclusion of the Coulomb interaction. The resulting excellent agreement between data and pure CD Bonn predictions in the FSI testifies to the smallness of three-nucleon force (3NF) effects as well as the insignificance of the Coulomb force for this particular configuration and energy. The CST also agrees well whereas the IST results show small deviations between measurements and theory seen before in the pd breakup space-star geometries which point to possible Coulomb effects. An additional comparison with effective field theory (EFT) predictions (without 3NF) up to order (NLO)-L-3 shows excellent agreement in the FSI case and a rather similar agreement as for CD Bonn in the CST and IST situations.
Different formulations of He-3 and H-3 photodisintegration
R. Skibiński, J. Golak, H. Witała, W. Glockle, A. Nogga
abstract
Different momentum space Faddeev-like equations and their solutions for the radiative pd-capture and the three-nucleon photodisintegration of He-3 are presented. Applications are based on the AV18 nucleon-nucleon and the Urbana IX three-nucleon forces. Meson exchange currents are included using the Siegert theorem. A very good agreement has been found in all cases indicating the reliability of the used numerical methods. Predictions for cross-sections and polarization observables in the pd-capture and the complete three-nucleon breakup of He-3 at different incoming-deuteron/photon energies are presented.
Analyzing power measurement in deuteron-proton breakup at 130 MeV
E. Stephan, A. Biegun, S. Kistryn, K. Bodek, W. Glockle, J. Golak, N. Kalantar-Nayestanaki, A. Kis, B. Klos, A. Kozela, J. Kuros-Zolnierczuk, A. Micherdzinska, M. Mahjour-Shafiei, R. Skibiński, R. Sworst, H. Witała, J. Zejma, W. Zipper
abstract
Vector and tensor analyzing powers of the H-1((d) over right arrow ,pp)n breakup process have been measured at the beam energy of 130 MeV. The forthcoming results will be compared with predictions based on various 2N and 3N forces models in quest for a correct structure of the 3NF.
Electron scattering on He-3 using momentum-space Faddeev techniques
J. Golak, R. Skibiński, H. Witała, W. Glockle, A. Nogga, H. Kamada
abstract
We present our new results on three-nucleon force effects for different observables at selected electron configurations below the pion production threshold. The results are compared to the experimental data and to very recent results by other groups based either on different techniques or on different three-nucleon dynamics.
Cross sections of the deuteron-proton breakup at 130 MeV
S. Kistryn, A. Biegun, E. Stephan, B. Klos, K. Bodek, K. Ermisch, W. Glockle, J. Golak, N. Kalantar-Nayestanaki, H. Kamada, M. Kis, A. Kozela, J. Kuros-Zolnierczuk, A. Micherdzinska, M. Mahjour-Shafiei, A. Nogga, R. Skibiniski, R. Sworst, H. Witała, J. Zejma, W. Zipper
abstract
Comparison of the cross sections measured over a large part of the phase space of the deuteron-proton breakup at 130 MeV with the results of rigorous, Faddeev-like calculations is presented. Global analysis, including nearly 1200 data points, reveals a better agreement for theoretical predictions which include three-nucleon force (3NF) model over the results obtained with only nucleon-nucleon realistic potentials. A possible way to probe details of the 3NF models via studying "non-standard" projections of the multi-dimensional phase space is envisaged.
Experimental search for evidence of the three-nucleon force and a new analysis method
P. Thorngren-Engblom, HO. Meyer, B. von Przewoski, J. Kuros-Zolnierczuk, TJ. Whitaker, J. Doskow, B. Lorentz, PV. Pancella, RE. Pollock, F. Rathmann, T. Rinckel, T. Wise, H. Witała, J. Golak, H. Kamada, A. Nogga, R. Skibiński
abstract
A research program with the aim of investigating the spin dependence of the three nucelon continuum in (p) over right arrow (d) over right arrow collisions at intermediate energies was carried out at IUCF using the Polarized INternal Target EXperiments (PINTEX) facility. In the, elastic scattering experiment at 135 and 200 MeV proton beam energies a total of 15 independent spin observables were obtained. The breakup experiment was done with a vector and tensor polarized deuteron beam of 270 MeV and an internal polarized hydrogen gas target. We developed a novel technique for the analysis of the breakup observables, the sampling method. The new approach takes into account acceptance and non-uniformities of detection efficiencies and is suitable for any kinematically complete experiment with three particles in the final state.
Photodisintegration of He-3 with polarized photons - predictions for a photon asymmetry
R. Skibiński, J. Golak, H. Witała, W. Glockle, A. Nogga
abstract
Measurement of the exclusive He-3(e,e ' p) reaction below the quasielastic peak
A. Kozlov, AJ. Sarty, KA. Aniol, P. Bartsch, D. Baumann, W. Bertozzi, K. Bohinc, R. Bohm, JP. Chen, D. Dale, L. Dennis, S. Derber, M. Ding, MO. Distler, P. Dragovitsch, I. Ewald, KG. Fissum, J. Friedrich, JM. Friedrich, R. Geiges, S. Gilad, P. Jennewein, M. Kahrau, M. Kohl, KW. Krygier, A. Liesenfeld, DJ. Margaziotis, H. Merkel, P. Merle, U. Muller, R. Neuhausen, T. Pospischil, M. Potokar, G. Riccardi, R. Roche, G. Rosner, D. Rowntree, H. Schmieden, S. Sirca, JA. Templon, MN. Thompson, A. Wagner, T. Walcher, M. Weis, J. Zhao, ZL. Zhou, J. Golak, W. Glockle, H. Witała
abstract
New, high-precision measurements of the He-3(e,e(')p) reaction using the A1 Collaboration spectrometers at the Mainz microtron MAMI are presented. These were performed in antiparallel kinematics at energy transfers below the quasielastic peak, and at a central momentum transfer of 685 MeV/c. Cross sections and distorted momentum distributions were extracted and compared to theoretical predictions and existing data. The longitudinal and transverse behavior of the cross section was also studied. Sizable differences in the cross-section behavior from theoretical predictions based on the plane wave impulse approximation were observed in both the two- and three-body breakup channels. Full Faddeev-type calculations account for some of the observed excess cross-section, but significant differences remain.
Limitations for the use of the spectral function in the semiexclusive He-3(e,e ' N) process
J. Golak, H. Witała, R. Skibiński, W. Glockle, A. Nogga, H. Kamada
abstract
The limitations for the use of the spectral function S in the process He-3(e,e(')N) has been investigated in a kinematical regime constrained by the conditions that the three-nucleon (3N) center-of-mass energy E(3N)(c.m.)less than or equal to150 MeV and the magnitude of the three-momentum transfer, (Q) over right arrowless than or equal to600 MeV/c. Results based on a full treatment of the final state interaction are compared to the spectral function approximation. In the case of proton knockout in the direction of the photon kinematical conditions have been identified where both response functions, R-L and R-T, can be well approximated by S. These conditions occur for certain low missing momenta and missing energies but not in all cases. So care is required. In case of neutron knockout only R-T is a candidate for an approximate treatment by S. In the case of R-L the concept of using S is not valid in the studied kinematical regime. This does not exclude the possibility that beyond that regime it might be useful. Possible applications using S for the extraction of electromagnetic form factors of the nucleons are pointed out.
Electron scattering on He-3 - A playground to test nuclear dynamics
W. Glockle, J. Golak, R. Skibiński, H. Witała, H. Kamada, A. Nogga
abstract
The electron-induced processes on He-3 are analyzed using the Faddeev formalism with modern nucleon-nucleon and three-nucleon forces as well as exchange currents. The kinematical region is restricted to a mostly nonrelativistic one where the three-nucleon c.m. energy is below the pion production threshold and the three-momentum of the virtual photon is sufficiently below the nucleon mass. Comparisons with available data are shown and cases of agreement and disagreement are found. It is argued that new and precise data are needed to systematically check the present-day dynamical ingredients.
Polarization transfer measurement for H-1((d)over-right-arrow,(p)over-right-arrow)H-2 elastic scattering at 135 MeV/nucleon and three-nucleon force effects
K. Sekiguchi, H. Sakai, H. Witała, K. Ermisch, W. Glockle, J. Golak, M. Hatano, H. Kamada, N. Kalantar-Nayestanaki, H. Kato, Y. Maeda, J. Nishikawa, A. Nogga, T. Ohnishi, H. Okamura, T. Saito, N. Sakamoto, S. Sakoda, Y. Satou, K. Suda, A. Tamii, T. Uchigashima, T. Uesaka, T. Wakasa, K. Yako
abstract
The deuteron-to-proton polarization-transfer coefficients for d-p elastic scattering were precisely measured with an incoming deuteron energy of 135 MeV/nucleon at the RIKEN Accelerator Research Facility. The data are compared to theoretical predictions based on exact solution's of the three-nucleon Faddeev equations with high-precision nucleon-nucleon forces combined with the current, most popular three-nucleon force (3NF) models: the 2pi-exchange Tucson-Melbourne model, a modification thereof based on chiral symmetry, TM'(99), and the Urbana IX 3NF. Theory predicts large 3NF effects, especially in the angular range around the cross sect. ion minimum, predominantly for K-xx(y')-K-yy(y')(K-xx(y'),K-yy(y')), but the present data only partially concurs with the calculations. For the induced polarization, P-y', the TM'(99) and Urbana IX 3NFs reproduce the data, but the Tucson-Melbourne 3NF fails to describe the data. For the polarization-transfer coefficients, K-y(y') and K-xz(y'), the predicted 3NF effects are in drastic disagreement with the data. These facts clearly reveal the defects of the 3NF models currently used.
Faddeev calculations of breakup reactions with realistic experimental constraints
J. Kuros-Zolnierczuk, PT. Engblom, HO. Meyer, TJ. Whitaker, H. Witała, J. Golak, H. Kamada, A. Nogga, R. Skibiński
abstract
We present a method to integrate predictions from a theoretical model of a reaction with three bodies in the final state over the region of phase space covered by a given experiment. The method takes into account the true experimental acceptance, as well as variations of detector efficiency, and eliminates the need for a Monte-Carlo simulation of the detector setup. The method is applicable to kinematically complete experiments. Examples for the use of this method include several polarization observables in dp breakup at 270 Mev The calculations are carried out in the Faddeev framework with the CD Bonn nucleon-nucleon interaction, with or without the inclusion of an additional three-nucleon force.
Systematic investigation of the elastic proton-deuteron differential cross section at intermediate energies
K. Ermisch, HR. Amir-Ahmadi, AM. van den Berg, R. Castelijns, B. Davids, E. Epelbaum, E. van Garderen, W. Glockle, J. Golak, MN. Harakeh, M. Hunyadi, MA. de Huu, N. Kalantar-Nayestanaki, H. Kamada, M. Kis, M. Mahjour-Shafiei, A. Nogga, R. Skibiński, H. Witała, HJ. Wortche
abstract
To investigate the importance of three-nucleon forces (3NF) systematically over a broad range of intermediate energies, the differential cross sections of elastic proton-deuteron scattering have been measured at proton bombarding energies of 108, 120, 135, 150, 170, and 190 MeV at c.m. angles between 30degrees and 170degrees . Comparisons with Faddeev calculations show unambiguously the shortcomings of calculations employing only two-body forces and the necessity of including 3NF. They also show the limitations of the latest few-nucleon calculations at backward angles, especially at higher beam energies. Some of these discrepancies could be partially due to relativistic effects. Data at lowest energy are also compared with a recent calculation based on chiPT .
Evidence of three-nucleon force effects from 130 MeV deuteron-proton breakup cross section measurement
S. Kistryn, A. Micherdzinska, R. Bieber, A. Biegun, K. Bodek, K. Ermisch, W. Glockle, J. Golak, N. Kalantar-Nayestanaki, H. Kamada, M. Kis, A. Kozela, J. Kuros-Zolnierczuk, A. Nogga, M. Mahjour-Shafiei, R. Skibiński, E. Stephan, H. Witała, J. Zejma, W. Zipper
abstract
The measurement of exclusive deuteron-proton breakup for kinematics covering a large fraction of the available phase space has been performed using 130 MeV deuteron beam. High precision fivefold cross section data in 38 kinematical configurations have been compared to predictions of modern nuclear forces. To this aim the three-nucleon (3N) Faddeev equations have been solved rigorously using the nucleon-nucleon (NN) potentials AV18, charge-dependent Bonn, Nijm I, and Nijm II alone, and combining them with the 2pi -exchange Tucson-Melbourne three-nucleon force (TM 3NF ) and with its modified version TM99, more consistent with chiral symmetry. The AV18 potential was also combined with the Urbana IX 3NF . Global comparison of the measured cross sections to pairwise NNforce predictions only and with 3NF 's included clearly reveals the presence of 3NF effects. Our study demonstrates the usefulness of the kinematically complete breakup reaction studied in the full phase space to search for 3NF effects.
Modern nuclear force predictions for the neutron-deuteron scattering lengths
H. Witała, A. Nogga, H. Kamada, W. Glockle, J. Golak, R. Skibiński
abstract
The neutron-deuteron (nd) doublet ((2)a(nd)) and quartet ((4)a(nd)) scattering lengths were calculated based on the nucleon-nucleon (NN) interactions CD Bonn 2000, AV18, Nijm I, II, and 93 alone and in selected combinations with the Tucson-Melbourne (TM), a modified version thereof, TM99, and the Urbana IX three-nucleon (3N) forces. For each NN and 3N force combination the H-3 binding energy was also calculated. In case of TM99 and Urbana IX the 3NF parameters were adjusted to the H-3 binding energy. In no case (using np-nn forces) the experimental value of (2)a(nd) was reached. We also studied the effect of the electromagnetic interactions in the form introduced in AV18. Switching them off for the various nuclear force models leads to shifts of up to +0.04 fm for (2)a(nd), which is significant for present day standards. The electromagnetic effects also have a noticeable effect on (4)a(nd), which is extremely stable under the exchange of the nuclear forces otherwise. Only if the electromagnetic interactions are included, the current nuclear forces describe the experimental value. As a consequence of the failure to reproduce (2)a(nd) also the newly measured coherent nd scattering length (b(nd)) cannot be reproduced. The current nuclear force models predict H-3 binding energies and the (2)a(nd) values around an averaged straight line (Phillips line), but this correlation is broken visibly. This allows us to use (2)a(nd) and the H-3 binding energy as independent low-energy observables.
The neutron charge form factor and target analyzing powers from (3)(He)over-right-arrow((e)over-right-arrow, e ' n) scattering
J. Bermuth, P. Merle, C. Carasco, D. Baumann, R. Bohm, D. Bosnar, M. Ding, MO. Distler, J. Friedrich, JM. Friedrich, J. Golak, W. Glockle, M. Hauger, W. Heil, P. Jennewein, J. Jourdan, H. Kamada, A. Klein, M. Kohl, B. Krusche, KW. Krygier, H. Merkel, U. Muller, R. Neuhausen, A. Nogga, C. Normand, E. Otten, T. Pospischil, M. Potokar, D. Rohe, H. Schmieden, J. Schmiedeskamp, M. Seimetz, I. Sick, S. Sirca, R. Skibiński, G. Testa, T. Walcher, G. Warren, M. Weis, H. Witała, H. Wohrle, M. Zeier
abstract
The charge form factor of the neutron has been determined from asymmetries measured in quasi-elastic 3 (He) over right arrow((e) over right arrow, e'n) at a momentum transfer of 0.67 (GeV/c)(2). In addition, the target analyzing power, A(y)(0), has been measured to study effects of final state interactions and meson exchange currents. (C) 2003 Published by Elsevier B.V.
Threshold electrodisintegration of He-3
RS. Hicks, A. Hotta, S. Churchwell, X. Jiang, GA. Peterson, J. Shaw, B. Asavapibhop, MC. Berisso, PE. Bosted, K. Burchesky, RA. Miskimen, SE. Rock, I. Nakagawa, T. Tamae, T. Suda, J. Golak, R. Skibiński, H. Witała, F. Casagrande, W. Turchinetz, A. Cichocki, K. Wang, W. Glockle, H. Kamada, T. Kobayashi, A. Nogga
abstract
Cross sections were measured for the near-threshold electrodisintegration of He-3 at momentum transfer values of q = 2.4, 4.4, and 4.7 fm(-1). From these and prior measurements the transverse and longitudinal response functions R-T and R-L were deduced. Comparisons are made against previously published and new nonrelativistic A = 3 calculations using the best available nucleon-nucleon NN potentials. In general, for <2 fm(-1) these calculations accurately predict the threshold electrodisintegration of He-3. Agreement at increasing q demands consideration of two-body terms, but discrepancies still appear at the highest momentum transfers probed, perhaps due to the neglect of relativistic dynamics, or to the underestimation of high-momentum wave-function components.
Effects of the magnetic moment interaction between nucleons on observables in the 3N continuum
H. Witała, J. Golak, R. Skibiński, CR. Howell, W. Tornow
abstract
The influence of the magnetic moment interaction of nucleons on nucleon-deuteron elastic scattering and breakup cross sections and on elastic scattering polarization observables has been studied. Among the numerous elastic scattering observables only the vector analyzing powers were found to show a significant effect, and of opposite sign for the proton-deuteron and neutron-deuteron systems. This finding results in an even larger discrepancy than the one previously established between neutron-deuteron data and theoretical calculations. For the breakup reaction the largest effect was found for the final-state-interaction cross sections. The consequences of this observation on previous determinations of the S-1(0) scattering lengths from breakup data are discussed.
Three-nucleon photodisintegration of He-3
R. Skibiński, J. Golak, H. Witała, W. Glockle, H. Kamada, A. Nogga
abstract
The three-nucleon (3N) photodisintegration of He-3 has been calculated in the whole phase space using consistent Faddeev equations for the three-nucleon bound and scattering states. Modern nucleon-nucleon and 3N forces have been applied, in addition to different approaches to nuclear currents. Phase space regions are localized where 3N force effects are especially large. In addition, semi-exclusive cross sections for He-3 (gamma,N), which carry interesting peak structures, have been predicted. Finally, some data for the exclusive 3N breakup process of He-3 and its total breakup cross section have been compared to theory.
Search for three-nucleon force effects in two-body photodisintegration of He-3 (H-3) and in the time reversed proton-deuteron radiative capture process
R. Skibiński, J. Golak, H. Kamada, H. Witała, W. Glockle, A. Nogga
abstract
Faddeev calculations have been performed for nucleon-deuteron photodisintegration of He-3 (H-3) and proton-deuteron radiative capture. The bulk of the results is based on the AV18 nucleon-nucleon force and the Urbana IX three-nucleon force together with explicit exchange currents or applying the Siegert approach. Three-nucleon force effects are predicted for both processes and are qualitatively supported by available data.
Final state interaction effects in (3)(He)over-right-arrow ((e)over-right-arrow, e ' p)
C. Carasco, J. Bermuth, P. Merle, P. Bartsch, D. Baumann, R. Bohm, D. Bosnar, M. Ding, MO. Distler, J. Friedrich, JM. Friedrich, J. Golak, W. Glockle, M. Hauger, W. Heil, P. Jennewein, J. Jourdan, H. Kamada, A. Klein, M. Kohl, KW. Krygier, H. Merkel, U. Muller, R. Neuhausen, A. Nogga, C. Normand, E. Otten, T. Pospischil, M. Potokar, D. Rohe, H. Schmieden, J. Schmiedeskamp, M. Seimetz, I. Sick, S. Sirca, R. Skibiński, G. Testa, T. Walcher, G. Warren, M. Weis, H. Witała, H. Wohrle, M. Zeier
abstract
Asymmetries in quasi-elastic (3)<(He)over right arrow>((e) over right arrow, e'p) have been measured at a momentum transfer of 0.67 (GeV/c)(2) and are compared to a calculation which takes into account relativistic kinematics in the final state and a relativistic one-body current operator. With an exact solution of the Faddeev equation for the He-3-ground state and an approximate treatment of final state interactions in the continuum good agreement is found with the experimental data. (C) 2003 Published by Elsevier Science B.V.
Testing the nuclear Hamiltonian in few-nucleon systems
H. Witała, E. Epelbaum, W. Glockle, J. Golak, H. Kamada, J. Kuros-Zolnierczuk, A. Nogga, R. Skibiński
abstract
Recent results on three-nucleon (3N) scattering are presented. The discrepancies between a theory based on numerical solutions of 3N Faddeev equations with NN interactions only and data point to the action of three-nucleon forces (3NF's). Also results of application of 3N bound and scattering states to photodisintegration of 3N bound states are shown.
Electron scattering from polarized He-3: Results of full Faddeev calculations
J. Golak, W. Glockle, H. Kamada, H. Witała, R. Skibiński, A. Nogga
abstract
We study within a Faddeev framework two processes, in which electrons (polarized or not) are scattered inelastically from polarized 3 He. For the helicity asymmetry A in the (3)(H) over right arrowe((e) over right arrow, e') process results of first calculations with a three-nucleon force are compared to recent data. Next, some predictions for the analyzing power A(0) in the process (3)(H) over right arrowe(e, e' N) are shown. Finally we consider the spin dependent momentum distributions in polarized He-3 from the reaction (3)(H) over right arrowe(e, e'(p) over right arrow).
Three-nucleon dynamics studied via H-1(d,pp)n breakup at 130 MeV
S. Kistryn, R. Bieber, A. Biegun, K. Bodek, K. Ermisch, W. Glockle, J. Golak, MN. Harake, N. Kalantar-Nayestanaki, H. Kamada, J. Kuros-Zolnierczuk, M. Kis, A. Micherdzinska, A. Nogga, M. Shafiei, R. Skibiński, E. Stephan, H. Witała, J. Zejma, W. Zipper
abstract
An experiment to measure cross sections and both, vector and tensor analyzing powers, for the H-1(d,pp)n breakup reaction at 130 MeV deuteron beam energy is presented. Employing a position-sensitive detection system covering a large solid angle enables probing of a significant part of the whole phase space. First results are presented and compared with the rigorous Faddeev calculations using modern NN and 3NF potentials.
Benchmark result on total three-nucleon photodisintegration
G. Orlandini, VD. Efros, W. Leidemann, EL. Tomusiak, J. Golak, R. Skibiński, W. Glockle, H. Kamada, A. Nogga, H. Witała
abstract
Cross section and complete set of proton spin observables in (p)over-right-arrow-d elastic scattering at 250 MeV
K. Hatanaka, Y. Shimizu, D. Hirooka, J. Kamiya, Y. Kitamura, Y. Maeda, T. Noro, E. Obayashi, K. Sagara, T. Saito, H. Sakai, Y. Sakemi, K. Sekiguchi, A. Tamii, T. Wakasa, T. Yagita, K. Yako, HP. Yoshida, VP. Ladygin, H. Kamada, W. Glockle, J. Golak, A. Nogga, H. Witała
abstract
The angular distributions of the cross section, the proton analyzing power, and all proton polarization transfer coefficients of pd elastic scattering were measured at 250 MeV. The range of center-of-mass angles was 10degrees-165degrees for the cross section and the analyzing power, and about 10degrees-95degrees for the polarization transfer coefficients. These are the first measurements of a complete set of proton polarization observables for pd elastic scattering at intermediate energies. The present data are compared with theoretical predictions based on exact solutions of the three-nucleon Faddeev equations and modern realistic nucleon-nucleon potentials combined with three-nucleon forces (3NF), namely, the Tucson-Melbourne (TM) 2pi-exchange model, a modification thereof (TM') closer to chiral symmetry, and the Urbana IX model. Large effects of the three-nucleon forces are predicted. The inclusion of the three-nucleon forces gives a good description of the cross section at angles below the minimum. However, appreciable discrepancies between the data and predictions remain at backward angles. For the spin observables the predictions of the TM 3NF model deviate strongly from the other two 3NF models, which are close together, except for K-y(y'). In the case of the analyzing power all 3NF models fail to describe the data at the upper half of the angular range. In the restricted measured angular range the polarization transfer coefficients are fairly well described by the TM' and Urbana IX 3NF models, whereas the TM 3NF model mostly fails. The transfer coefficient K-y(y') is best described by the Urbana IX but the theoretical description is still insufficient to reproduce the experimental data. These results call for a better understanding of the spin structure of the three-nucleon force and very likely for a full relativistic treatment of the three-nucleon continuum.
Benchmark calculation of the three-nucleon photodisintegration
J. Golak, R. Skibiński, W. Glockle, H. Kamada, A. Nogga, H. Witała, VD. Efros, W. Leidemann, G. Orlandini, EL. Tomusiak
abstract
A benchmark is set on the three-nucleon photodisintegration calculating the total cross section with modem realistic two- and three-nucleon forces using both the Faddeev equations and the Lorentz integral transform method. This test shows that the precision of three-body calculations involving continuum states is considerably higher than experimental uncertainties. Effects due to retardations, higher multipoles, meson exchange currents and Coulomb force are studied. (C) 2002 Elsevier Science B.V. All rights reserved.
The He-3(e, e ' d)p reaction in (q, omega)-constant kinematics
CM. Spaltro, TS. Bauer, HP. Blok, T. Botto, E. Cisbani, R. De Leo, GE. Dodge, R. Ent, S. Frullani, F. Garibaldi, W. Glockle, J. Golak, MN. Harakeh, M. Iodice, E. Jans, H. Kamada, WJ. Kasdorp, C. Kormanyos, L. Lapikas, A. Misiejuk, SI. Nagorny, GJ. Nooren, CJG. Onderwater, R. Perrino, M. van Sambeek, R. Skibiński, R. Starink, G. van der Steenhoven, J. Tjon, MA. van Uden, GM. Urciuoli, H. de Vries, H. Witała, M. Yeomans
abstract
The cross section for the He-3(e, c' d)p reaction has been measured as a function of the missing momentum p(m) in (q, omega)-constant kinematics at beam energies of 370 and 576 MeV for values of the three-momentum transfer q of 412, 504 and 604 MeV/c. The L(+ TT), T and LT structure functions have been separated for q = 412 and 504 MeV/c. The data are compared to three-body Faddeev calculations, including meson-exchange currents (MEC), and to calculations based on a covariant diagrammatic expansion. The influence of final-state interactions and meson-exchange currents is discussed. The p(m)-dependence of the data is reasonably well described by all calculations. However, the most advanced Faddeev calculations, which employ the AV 18 nucleon-nucleon interaction and include MEC, overestimate the measured cross sections, especially the longitudinal part, and at the larger values of q. The diagrammatic approach gives a fair description of the cross section, but under(over)estimates the longitudinal (transverse) structure function. (C) 2002 Elsevier Science B.V. All rights reserved.
Theoretical predictions for extraction of G(E)(n) from semi-inclusive electron scattering on polarized He-3 based on various nucleon-nucleon interactions
J. Golak, W. Glockle, H. Kamada, H. Witała, R. Skibiński, A. Nogga
abstract
The process (3)(H) over right arrowe((e) over right arrow ,e(')n) is theoretically analyzed with the aim to search for sensitivity to the electric form factor of the neutron, G(E)(n). Faddeev calculations based on five high precision nucleon-nucleon force models are employed, and stability versus exchange of the nucleon-nucleon forces is demonstrated.
Three-nucleon force effects in nucleon induced deuteron breakup. II. Comparison to data
J. Kuros-Zolnierczuk, H. Witała, J. Golak, H. Kamada, A. Nogga, R. Skibiński, W. Glockle
abstract
Selected Nd breakup data over a wide energy range are compared to solutions of Faddeev equations based on modern high precision NN interactions alone and adding current three-nucleon force models. Unfortunately currently available data probe phase space regions for the final three nucleon momenta which are rather insensitive to three-nucleon force (3NF) effects as predicted by current models. Overall there is good to fair agreement between present day theory and experiment but also some cases exist with striking discrepancies. Regions in the phase space are suggested where large 3NF effects can be expected.
Three-nucleon force effects in nucleon induced deuteron breakup. I. Predictions of current models
J. Kuros-Zolnierczuk, H. Witała, J. Golak, H. Kamada, A. Nogga, R. Skibiński, W. Glockle
abstract
An extensive study of three-nucleon force effects in the entire phase space of the nucleon-deuteron breakup process, for energies from above the deuteron breakup threshold up to 200 MeV, has been performed. 3N Faddeev equations have been solved rigorously using the modern high precision nucleon-nucleon potentials AV18, CD Bonn, Nijm I, II, and Nijm 93, and also adding 3N forces. We compare predictions for cross sections and various polarization observables when NN forces are used alone or when the 2pi-exchange Tucson-Melbourne (TM) three nucleon force (3NF) was combined with each of them. In addition AV18 was combined with the Urbana IX 3NF and CD Bonn with the TM' 3NF, which is a modified version of the TM 3NF, more consistent with chiral symmetry. Large but generally model dependent 3NF effects have been found in certain breakup configurations, especially at the higher energies, both for cross sections and spin observables. These results demonstrate the usefulness of the kinematically complete breakup reaction in testing the proper structure of 3N forces.
Spin dependent momentum distributions of proton-deuteron clusters in He-3 from electron scattering on polarized He-3: Theoretical predictions
J. Golak, W. Glockle, H. Kamada, H. Witała, R. Skibiński, A. Nogga
abstract
The process (He-3) over right arrow (e,e'p)d [or (He-3) over right arrow (e,e'(d) over right arrow )p] is studied theoretically in a Faddeev treatment with the aim to have access to the spin dependent momentum distribution of (p) over right arrow (d) over right arrow clusters in polarized He-3. Final state interactions and meson exchange currents turn out to have a strong influence in the considered kinematical regime (below the pion threshold). This precludes direct access to the momentum distribution except for small deuteron momenta. Nevertheless, the results for the longitudinal and transverse response functions are interesting as they reflect our present day understanding of the reaction mechanism and therefore data would be very useful.
Sensitivity studies for extraction of G(E)(n) from inclusive and semi-inclusive electron scattering on polarized He-3
J. Golak, W. Glockle, H. Kamada, H. Witała, R. Skibiński, A. Nogga
abstract
The processes (He-3) over right arrow((e) over right arrow ,e(')) and (He-3) over right arrow((e) over right arrow ,e' n) are theoretically analyzed with the aim to search for sensitivities in the electric form factor of the neutron, G(E)(n). Faddeev calculations based on the high-precision NN force AV18 and using consistent mesonic exchange currents are employed. While the inclusive process is too insensitive, the semiexclusive one appears promising.
Complete set of precise deuteron analyzing powers at intermediate energies: Comparison with modern nuclear force predictions
K. Sekiguchi, H. Sakai, H. Witała, W. Glockle, J. Golak, M. Hatano, H. Kamada, H. Kato, Y. Maeda, J. Nishikawa, A. Nogga, T. Ohnishi, H. Okamura, N. Sakamoto, S. Sakoda, Y. Satou, K. Suda, A. Tamii, T. Uesaka, T. Wakasa, K. Yako
abstract
Precise measurements of deuteron vector and tensor analyzing powers A(y)(d), A(xx), A(yy), and A(xz) in d-p elastic scattering were performed via H-1((d) over bar ,d) p and H-1((d) over right arrow ,p)d reactions at three incoming deuteron energies of E-d(lab) = 140, 200, and 270 MeV. A wide range of center-of-mass angles from approximate to10degrees to 180degrees was covered. The cross section was measured at 140 and 270 MeV at the same angles. These high precision data were compared with theoretical predictions based on exact solutions of three-nucleon Faddeev equations and modern nucleon-nucleon potentials combined with three-nucleon forces. Three-body interactions representing a wide range of present day models have been used: the Tucson-Melbourne 2pi-exchange model, a modification thereof closer to chiral symmetry, the Urbana IX model, and a phenomenological spin-orbit ansatz. Large three-nucleon force effects are predicted, especially at the two higher energies. However, only some of them, predominantly dsigma/dOmega and A(y)(d), are supported by the present data. For tensor analyzing powers the predicted effects are in drastic conflict to the data, indicating defects of the present day three-nucleon force models.
Testing the nuclear Hamiltonian in the 3N continuum and the electromagnetic processes on H-3
H. Witała, W. Glockle, J. Golak, H. Kamada, J. Kuros-Zolnierczuk, A. Nogga, R. Skibiński
abstract
Recent results on three-nucleon (3N) scattering below the pion production threshold are presented with emphasis on the need of a three-nucleon force (3NF). The large discrepancies between a theory based on numerical solutions of 3N Faddeev equations with modem NN interactions only and data clearly point to the action of 3NF's. Successes and failures in the description of high precision 3N data using in addition some of the present day 3NF models are discussed. The large theoreticaly 3NF effects for different 3N polarization observables nourish the hope to pin down the proper spin structure of 3NF's. In addition, as an application of 3N bound and scattering states new results for photodisintegration of 3N bound states are shown.
Few-nucleon calculations and correlations
W. Glockle, H. Kamada, J. Golak, A. Nogga, H. Witała, R. Skibiński, J. Kuros-Zolnierczuk
abstract
Present day results for few-nucleon bound state and scattering observables based on modern high precision nuclear forces are briefly reviewed. While in relation to NN forces of that type three-nucleon (3N) forces are mandatory for binding energies and for quite a few 3N scattering observables their effect is rather small in two-nucleon correlation functions as demonstrated for He-3 and He-4. The old idea of the Coulomb sum rule as a way to extract the pp correlation function is reconsidered and the need for more accurate data is pointed out. It appears to be an ideal case to probe properties of the density operator and the ground state wave functions without disturbances of final state interactions (FSI). In the 3N system below the pion threshold FSI is well under control and therefore the exclusive process He-3(e, e'NN) is also a very good test case for correlated nuclear wave functions and electromagnetic current operators. One specific kinematics is emphasized, which can lead to insights into the correlated ground state wave functions with little disturbance of FSI. Finally exclusive photodisintegration of He-3 is regarded, which appears to be promising to identify 3N force effects.
Search for three-nucleon force effects in analyzing powers for (p)over-right-arrowd elastic scattering
K. Ermisch, AM. van den Berg, R. Bieber, W. Glockle, J. Golak, M. Hagemann, VM. Hannen, MN. Harakeh, MA. de Huu, N. Kalantar-Nayestanaki, H. Kamada, M. Kis, J. Kuros-Zolnierczuk, M. Mahjour-Shafiei, A. Micherdzinska, A. Nogga, R. Skibiński, H. Witała, HJ. Wortche
abstract
A series of measurements have been performed at KVI to obtain the vector analyzing power Ay Of the H-2((p) over right arrow, pd) reaction as a function of incident beam energy at energies of 120, 135, 150, and 170 MeV. For all these measurements, a range of upsilon (c.m) from 30 degrees to 170 degrees has been covered. The purpose of these investigations is to observe possible spin-dependent effects beyond two-nucleon forces. When compared to the,predictions of Faddeev calculations, based on two-nucleon forces only, significant deviations are observed at all energies and at center-of-mass angles between 70 degrees and 130 degrees. The addition of present-day three-nucleon forces does not improve the description of the data, demonstrating the still insufficient understanding of the properties of three-nucleon systems.
Selected electromagnetic processes in three-nucleon systems
J. Golak, H. Kamada, H. Witała, W. Glockle, G. Ziemer, J. Kuros, R. Skibiński, VV. Kotlyar
abstract
The central dynamical ingredient for electromagnetic processes in three-nucleon systems is the nuclear current operator. It consists of a single nucleon part and more than one-nucleon parts. Due to the spin structure of the He-3 wave function, polarized He-3 targets are used as effective neutron targets with the aim to extract the magnetic (G(M)(n)) and electric (G(E)(n)) neutron form factors at certain Q(2) values. In this talk we present an analysis of two recent experiments [1,2] on the processes He-3((e) over right arrow, e ') and He-3((e) over right arrow, e 'n). This theoretical analysis is based on E'addeev solutions for the three-nucleon continuum and the three-nucleon bound state belonging to the same three-nucleon Hamiltonian [3-5]. We use realistic, nucleon-nucleon forces and incorporate mesonic exchange currents [6]. The analysis [7] of the exclusive experiment by consistent Faddeev solutions for the three-nucleon continuum and 3He has not been done before to the best of our knowledge. Extracted values for G(M)(n) in case of the inclusive process and Gn, in case of the exclusive process agree well with the ones extracted from processes on the deuteron. Within the same framework we investigate the proton-deuteron radiative capture process at various energies. The application of the Siegert theorem is compared to the explicit use of pi- and rho -like exchange currents connected to the Argonne nucleon-nucleon potentials. Good agreement with cross sections and spin observables is obtained. We demonstrate that the different modern nucleon-nucleon forces taken together with the Siegert theorem give essentially the same predictions.
Three-nucleon force effects in the dp-breakup at 130 MeV
S. Kistryn, R. Bieber, K. Bodek, K. Ermisch, W. Glockle, J. Golak, MN. Harakeh, N. Kalantar-Nayestanaki, J. Kuros-Zolnierczuk, H. Kamada, A. Micherdzinska, A. Nogga, R. Skibiński, M. Sokolowski, E. Stephan, A. Strzalkowski, H. Witała, J. Zejma, W. Zipper
abstract
Indications for three nucleon force (3NF) effects in PJd elastic scattering and in specific kinematical configurations of the deuteron breakup reaction became motivation for complex studies of the three nucleon system dynamics in the dp breakup process over a broad region of phase-space. A dedicated experiment is aimed at precise determination of cross sections and both vector and tenser analyzing powers for the H-1((p) over right arrow pp)n breakup reaction at 130 MeV deuteron beam energy. The experiment, employs a position-sensitive detection system covering a large solid angle and allowing for excellent particle identification. The first data taking run has been completed and the accumulated data are being analyzed. The results will be compared with the rigorous calculations within the Faddeev formalism, including various nucleon-nucleon potentials and 3NF models.
Selected topics in few-nucleon physics
W. Glockle, H. Witała, H. Kamada, J. Golak, A. Nogga, G. Ziemer
abstract
Search for three-nucleon force effects in dp-breakup reaction
R. Bieber, K. Bodek, K. Ermisch, W. Glockle, J. Golak, MN. Harakeh, N. Kalantar-Nayestanaki, S. Kistryn, J. Kuros-Zolnierczuk, J. Lang, A. Micherdzinska, R. Skibiński, M. Sokolowski, J. Sromicki, E. Stephan, A. Strzalkowski, M. Volkerts, H. Witała, J. Zejma, W. Zipper
abstract
Faddeev calculations of proton-deuteron radiative capture with pi- and rho-meson exchange currents of the Argonne potentials
H. Kamada, J. Golak, H. Witała, W. Glockle, J. Kuros, R. Skibiński, VV. Kotlyar
abstract
A(y) puzzle at intermediate energy pd elastic scattering
N. Kalantar-Nayestanaki, R. Bieber, W. Glockle, J. Golak, MN. Harakeh, H. Huisman, H. Kamada, JG. Messchendorp, A. Nogga, H. Sakai, N. Sakamoto, M. Volkerts, SY. van der Werf, H. Witała
abstract
Extraction of electromagnetic neutron form factors through inclusive and exclusive polarized electron scattering on a polarized He-3 target
J. Golak, G. Ziemer, H. Kamada, H. Witała, W. Glockle
abstract
Data for the inclusive process (He-3) over right arrow((e) over right arrowe') have been theoretically analyzed and values for the magnetic and electric neutron form factors have been extracted at Q(2) = 0.1 and 0.2 GeV2/c(2). Similarly a theoretical analysis has been carried through for the process (He-3) over right arrow((e) over right arrow ,e' n) and the value of the electric neutron form factor has been extracted around Q(2) = 0.4 GeV2/c(2). In both cases the form factor values agree well with the ones extracted from processes on the deuteron. Our results are based on Faddeev solutions, modem NN forces, and partially on the incorporation of mesonic exchange currents.
Evidence for a three-nucleon-force effect in proton-deuteron elastic scattering
RV. Cadman, J. Brack, WJ. Cummings, JA. Fedchak, BD. Fox, H. Gao, W. Glockle, J. Golak, C. Grosshauser, RJ. Holt, CE. Jones, H. Kamada, ER. Kinney, MA. Miller, W. Nagengast, A. Nogga, BR. Owen, K. Rith, F. Schmidt, EC. Schulte, J. Sowinski, F. Sperisen, EL. Thorsland, R. Tobey, J. Wilbert, H. Witała
abstract
Developments in spin-polarized internal targets for storage rings have permitted measurements of 197 MeV polarized protons scattering from vector polarized deuterons. This work presents measurements of the polarization observables A(gamma), iT(11), and C-gamma,C-gamma in proton-deuteron elastic scattering. When compared to calculations with and without three-nucleon forces, the measurements provide further evidence that three-nucleon forces make a contribution to the observables. This work indicates that three-body forces derived from static nuclear properties appear to be crucial to the description of dynamical properties.
Nd elastic scattering as a tool to probe properties of 3N forces
H. Witała, W. Glockle, J. Golak, A. Nogga, H. Kamada, R. Skibiński, J. Kuros-Zolnierczuk
abstract
Faddeev equations for elastic Nd scattering have been solved using modern NN forces combined with the Tucson-Melbourne two-pion exchange three-nucleon force, with a modification thereof closer to chiral symmetry and the Urbana IX three-nucleon force. Theoretical predictions for the differential cross section and several spin observables using NN forces only and NN forces combined with three-nucleon force models are compared to each other and to the existing data. A wide range of energies from 3 to 200 MeV is covered. Especially at the higher energies striking three-nucleon force effects are found, some of which are supported by the still rare set of data, some of which are in conflict with data and thus very likely point to defects in those three-nucleon force models.
Investigation of the exclusive He-3(e,e ' pp)n reaction
DL. Groep, MF. van Batenburg, TS. Bauer, HP. Blok, DJ. Boersma, E. Cisbani, R. De Leo, S. Frullani, F. Garibaldi, W. Glockle, J. Golak, P. Heimberg, WHA. Hesselink, M. Iodice, DG. Ireland, E. Jans, H. Kamada, L. Lapikas, GJ. Lolos, CJG. Onderwater, R. Perrino, A. Scott, R. Starink, MFM. Steenbakkers, GM. Urciuoli, H. de Vries, LB. Weinstein, H. Witała
abstract
Cross sections for the He-3(e,e'pp)n reaction were measured over a wide range of energy and three-momentum transfer. At a momentum transfer q=375 MeV/c, data were taken at transferred energies omega ranging from 170 to 290 MeV. At omega = 220 MeV, measurements were performed at three q values (305, 375, and 445 MeV/c). The results are presented as a function of the neutron momentum in the final state, as a function of the energy and momentum transfer, and as a function of the relative momentum of the two-proton system. The data at neutron momenta below 100 MeV/c, obtained for two values of the momentum transfer at omega = 220 MeV, are well described by the results of continuum-Faddeev calculations. These calculations indicate that the cross section in this domain is dominated by direct two-proton emission induced by a one-body hadronic current. Cross section distributions determined as a function of the relative momentum of the two protons are fairly well reproduced by continuum-Faddeev calculations based on various realistic nucleon-nucleon potential models. At higher neutron momentum and at higher energy transfer, deviations between data and calculations are observed that may be due to contributions of isobar currents.
Systematics of the H-2((p)over-right-arrow,pp)n reaction between 10.3 and 19.0 MeV
HPG. Schieck, H. Witała, J. Golak, J. Kuros, R. Skibiński
abstract
The H-2((p) over right arrow, pp)n breakup reaction has been investigated in the past at several tandem accelerator energies below 20 MeV in a number of "classical" kinematical configurations, These data are compared with predictions of four modern high-precision nucleon-nucleon potentials, calculated for H-2(n, np)n, i.e., without inclusion of the Coulomb interaction. The results show a remarkably good agreement between data and theory in some situations such as the final-state interaction, indicating the smallness of three-nucleon-force effects as well as the insignificance of the Coulomb force for this particular configuration, Other configurations such as the symmetric space-star or quasi-free scattering are not well described, The discrepancies cannot be removed by including into three-nucleon Faddeev calculations the 2 pi -exchange Tucson-Melbourne three-nucleon force with the cutoff parameter adjusted individually for each nucleon-nucleon interaction to fit the experimental triton binding energy. In contrast to quasi-free or symmetric space-star scattering configurations a comparison with corresponding neutron-deuteron data shows that this discrepancy cannot be traced back to the missing Coulomb interaction.
Proton-induced deuteron breakup reaction at 65 MeV: Unspecific configurations
K. Bodek, J. Golak, L. Jarczyk, S. Kistryn, J. Kuros-Zolnierczuk, J. Lang, A. Micherdzinska, R. Skibiński, J. Smyrski, M. Sokolowski, J. Sromicki, A. Strzalkowski, H. Witała, J. Zejma, W. Zipper
abstract
Cross sections and vector-analyzing powers for four unspecific configurations of the H-2(p,pp)yl breakup reaction at E-p(lab) = 65 MeV were measured in a kinematically complete experiment. Measured observables are compared with rigorous Faddeev calculations using four realistic charge-dependent interaction models, the CD Bonn, Argonne upsilon (18), Nijmegen I, and Nijmegen II potentials with or without inclusion of the Tucson-Melbourne three-nucleon force. Coulomb effects are completely omitted. A satisfactory agreement between theory and experiment has been found. There exist, however, some discrepancies between measured and calculated analyzing-power distributions in certain kinematical regions. The effects of the Tucson-Melbourne three-body force are either negligible or slightly increasing the disagreement.
Three-nucleon spin observables: signatures for three-nucleon force effects
H. Witała, W. Glockle, H. Kamada, A. Nogga, J. Golak, J. Kuros-Zohnierczuk, R. Skibiński
abstract
The numerical solutions of three-nucleon (3N) Faddeev equations with modern, high precision nucleon-nucleon (NN) interactions are compared to new nucleon-deuteron (Nd) data at nucleon laboratory energies between 100 and 200 MeV. The large discrepancies between theory and data clearly point to the action of three-nucleon forces (3NF). Successes and failures in the description of those data using in addition different, present day 3NF models are described. This indicates flaws in the present day 3NF models. However the large 3NF effects found theoretically for different 3N spin observables are promising to pin down the proper spin structure of 3NF's.
Proton-induced deuteron breakup reaction at 65 MeV: Unspecific configurations
K. Bodek, J. Golak, L. Jarczyk, S. Kistryn, J. Kuros-Zolnierczuk, J. Lang, A. Micherdzinska, R. Skibinski, J. Smyrski, M. Sokolowski, J. Sromicki, A. Strzalkowski, H. Witala, J. Zejma, W. Zipper
abstract
Cross sections and vector-analyzing powers for four unspecific configurations of the H-2(p,pp)yl breakup reaction at E-p(lab) = 65 MeV were measured in a kinematically complete experiment. Measured observables are compared with rigorous Faddeev calculations using four realistic charge-dependent interaction models, the CD Bonn, Argonne upsilon (18), Nijmegen I, and Nijmegen II potentials with or without inclusion of the Tucson-Melbourne three-nucleon force. Coulomb effects are completely omitted. A satisfactory agreement between theory and experiment has been found. There exist, however, some discrepancies between measured and calculated analyzing-power distributions in certain kinematical regions. The effects of the Tucson-Melbourne three-body force are either negligible or slightly increasing the disagreement.
Faddeev calculations of proton-deuteron radiative capture with exchange currents
J. Golak, H. Kamada, H. Witała, W. Glockle, J. Kuros-Zolnierczuk, R. Skibiński, VV. Kotlyar, K. Sagara, H. Akiyoshi
abstract
pd capture processes at various energies have been analyzed based on solutions of three-nucleon (3N)-Faddeev equations and using modern NN forces. The application of the Siegert theorem is compared to the explicit use of pi- and rho -like exchange currents connected to the AV18 NN interaction. Overall good agree ment with cross sections and spin observables has been obtained but leaving room for improvement in some cases. Feasibility studies for three-nucleon forces (3NF's) consistently included in the 3N continuum and the 3N bound state have been performed as well.
Three-nucleon force and the A(y) puzzle in intermediate energy (p)over-right-arrow+d and (d)over-right-arrow+p elastic scattering
R. Bieber, W. Glockle, J. Golak, MN. Harakeh, D. Huber, H. Huisman, N. Kalantar-Nayestanaki, H. Kamada, JG. Messchendorp, A. Nogga, H. Sakai, N. Sakamoto, M. Seip, M. Volkerts, SY. van der Werf, H. Witała
abstract
New vector analyzing-power data on (p) over right arrow+ d elastic scattering at E-p = 150 and 190 MeV have been measured. These an presented together with existing data and with recent (d) over right arrow + p vector and tensor analyzing power data at E-d = 270 MeV. The strong negative extremum of both vector analyzing powers A(y)(p) and A(y)(d) at theta(c.m.) similar or equal to 80 degrees-120 degrees is underestimated by Faddeev calculations using modern NN forces. Inclusion of the Tucson-Melbourne 3N force shifts the minima upwards, but with conflicting results for p A(y)(p), and leading to a good description for A(y)(d). An A(y)(p) puzzle, previously thought to exist at energies E-N less than or equal to 30 MeV only, appears to exist also at intermediate energies.
Three-nucleon scattering: New physical insights and applications
H. Witała, W. Glockle, J. Golak, H. Kamada, A. Nogga
abstract
Recent results on three-nucleon (3N) scattering below the pion production threshold are reviewed. New physical insights on the role played by a three nucleon force (3NF) and present experimental evidence for it will be discussed by comparing new, high precision 3N data and theory based on modern nucleon-nucleon (NN) forces and including the 2 pi -exchange Tucson Melbourne (TM) 3NF. As an application of 3N bound and scattering states new results for the pd capture reaction will be presented. They are based on an improved nuclear current which includes pi and rho meson exchange contributions. First results for the effects of 3NF's in the pd capture process will be shown.
Sensitivity of the low-energy p-d capture observables to the P-3(j) nucleon-nucleon force components
J. Golak, H. Witała
abstract
Polarization observables in low-energy proton-deuteron radiative capture have been calculated using the Bonn-B nucleon-nucleon potential. Their sensitivity to the changes of the P-3(j) nucleon-nucleon force components has been studied. Modifications of these forces, which drastically diminished the permanent discrepancy between the data and theory for the vector-analyzing power in low-energy nucleon-deuteron elastic scattering, have only small effects on the pd capture observables.
Investigation of the exclusive He-3(e,e ' pp)n reaction
DL. Groep, MF. van Batenburg, TS. Bauer, HP. Blok, DJ. Boersma, E. Cisbani, R. De Leo, S. Frullani, F. Garibaldi, W. Glockle, J. Golak, P. Heimberg, WHA. Hesselink, M. Iodice, DG. Ireland, E. Jans, H. Kamada, L. Lapikas, GJ. Lolos, R. Perrino, A. Scott, R. Starink, MFM. Steenbakkers, GM. Urciuoli, H. de Vreis, LB. Weinstein, H. Witała
abstract
Cross sections for the He-3(e, e'pp)n reaction were measured at an energy transfer of 220 MeV and three-momentum transfers q of 305, 375, and 445 MeV/c. Results are presented as a function of q and the final-state neutron momentum for slices in specific :kinematic variables. At low neutron momenta, comparison of the data to results of continuum Faddeev calculations performed with the Bonn-B nucleon-nucleon potential indicates a dominant role for two-proton knockout induced by a one-body.
np final-state interaction in the reaction H-2((p)over-right-arrow,pp)n at E(p)over-right-arrow=19 MeV
M. Przyborowski, M. Eggert, R. Engels, M. Menzel, L. Sydow, HPG. Schieck, H. Witała, J. Golak, J. Kuros, W. Glockle
abstract
We investigated the H-2((p) over right arrow, pp)n breakup reaction by measuring an angular distribution of the cross section and analyzing power in the np final-state interaction (FSI) at E-(p) over right arrow = 19 MeV as a function of the np production angle. Kinematically complete measurements at 12 angular settings of detectors have been done. The observables around the exact FSI point were compared with predictions of four modern NN potentials, calculated for H-2(n, np)n, i.e., without inclusion of the Coulomb interaction. The resulting good overall agreement between the data and theory indicates the smallness of three-nucleon force (3NF) effects as well as the insignificance of the Coulomb force for this particular configuration and energy. This conclusion is supported by results of three-nucleon (3N) Faddeev calculations performed with 2 pi-exchange Tucson-Melbourne 3NF with cutoff parameter adjusted individually for each NN interaction to fit the experimental triton binding. [S0556-2813(99)05612-5].
Impossibility to measure the total neutron- and proton-induced nonmesonic decays for H-3(Lambda)
J. Golak, H. Kamada, K. Miyagawa, H. Witała, W. Glockle
abstract
Based on realistic calculations for the nonmesonic(-)decay rate of (3)Lambda H we demonstrate that, in principle, it is not possible to measure the total n- and p-induced decay rates and as a consequence Gamma(n)/Gamma(p) for that lightest hypernucleus. The calculations are performed with modern YN fords based on various meson exchanges and taking the final state interaction among the three nucleons fully into account. Our findings might have consequences also for the interpretation of experimental Gamma(n)/Gamma(p) ratios for heavier hypernuclei where severe discrepancies exist to theoretical Gamma(n)/Gamma(p) ratios.
Polarization transfer in H-2((p)over-right-arrow,(n)over-right-arrow)pp
M. Zeier, H. Anklin, S. Buttazzoni, W. Glockle, J. Golak, A. Honegger, J. Jourdan, H. Muhry, T. Petitjean, I. Sick, H. Witała, B. Zihlmann
abstract
We measured the 0 degrees polarization transfer of the H-2((p) over right arrow, (n) over right arrow)pp reaction used to produce a high-intensity, monoenergetic neutron beam. The 0(+) --> 0(+) reaction C-14((p) over right arrow, (n) over right arrow)N-14(2.31) has been used to calibrate a high-efficiency polarimeter, which in turn was used to measure the polarization transfer in H-2((p) over right arrow (n) over right arrow)pp. With this data the uncertainty on the polarization of the 70 MeV neutron beam, used for many different studies at PSI, is reduced to 1.1%. The data are compared to predictions of Faddeev calculations based on realistic nucleon-nucleon interactions. (C) 1999 Elsevier Science B.V. All rights reserved.
Electron-induced two-proton knockout from He-3
DL. Groep, MF. van Batenburg, TS. Bauer, HP. Blok, DJ. Boersma, E. Cisbani, R. De Leo, S. Frullani, F. Garibaldi, W. Glockle, J. Golak, P. Heimberg, WHA. Hesselink, M. Iodice, DG. Ireland, E. Jans, H. Kamada, L. Lapikas, G. Lolos, R. Perrino, A. Scott, R. Starink, MFM. Steenbakkers, GM. Urciuoli, H. de Vries, LB. Weinstein, H. Witała
abstract
Final state interaction effects in mu-capture induced two-body decay of He-3
R. Skibiński, J. Golak, H. Witała, W. Glockle
abstract
The mu-capture process on He-3 leading to a neutron, a deuteron, and a mu-neutrino in the final state is studied. Three-nucleon Faddeev wave functions for the initial He-3 bound and the final neutron-deuteron scattering states are calculated using the Bonn B and Paris nucleon-nucleon potentials. The nuclear weak current operator is restricted to the impulse approximation. Large effects on the decay rates of the final state interaction are found. The comparison to recent experimental data shows that the inclusion of final state interactions drastically improves the description of the data. [S0556-2813(99)04805-0].
Scaling properties of the longitudinal and transversal asymmetries of the (n)over-right-arrow(d)over-right-arrow total cross section
H. Witała, W. Glockle, J. Golak, D. Huber, H. Kamada, A. Nogga
abstract
The longitudinal and transversal asymmetries of the total (n) over right arrow d cross section are calculated. Four modern nucleon-nucleon interactions: AV18. CD Bonn, NijmI and NijmII, give different predictions for these observables. When the three-nucleon Hamiltonian is supplemented by the 2 pi-exchange Tucson-Melbourne three-nucleon force (3NF), individually adjusted with each particular NN potential to reproduce the experimental triton binding energy, all predictions practically coincide. We propose to check this scaling behavior experimentally in order to get a clear signal for 3NF effects in the low energy three-nucleon continuum. Connected to that is the proposal to measure the energy at which the longitudinal asymmetry goes through zero. This energy is shifted by about 400 keV when 3NF's are acting. (C) 1999 Elsevier Science B.V. All rights reserved.
Pionic decay of the hypertriton
H. Kamada, J. Golak, K. Miyagawa, H. Witała, W. Glockle
abstract
The pionic decay of the hypertriton is investigated. Three-body Faddeev equations are rigorously solved for the bound state and scattering states using realistic NN and YN interactions. The theoretically predicted decay rates agree well with experiment.
Effects of final state interaction in the He-3 decay caused by muon capture.
R. Skibiński, W. Glockle, J. Golak, H. Witała
abstract
The He-3 decay caused by mu-capture leading to neutron, deuteron and mu-neutrino in outgoing channel is investigated. Three-nucleon Faddeev wave functions for the both initial and final states are calculated using the Bonn B and Paris nucleon-nucleon potentials. Large effects of interactions between nucleons in the final state on the decay rate are found and comparison to recent experimental data shows a nice agreement for full calculations.
Electron-induced two-proton knockout from He-3
DL. Groep, MF. van Batenburg, TS. Bauer, HP. Blok, DJ. Boersma, E. Cisbani, R. De Leo, S. Frullani, F. Garibaldi, W. Glockle, J. Golak, P. Heimberg, WHA. Hesselink, M. Iodice, D. Ireland, E. Jans, H. Kamada, L. Lapikas, G. Lolos, R. Perrino, A. Scott, R. Starink, MFM. Steenbakkers, GM. Urciuoli, H. de Vries, LB. Weinstein, H. Witała
abstract
Benchmark calculations for polarization observables in three-nucleon scattering
A. Kievsky, M. Viviani, S. Rosati, D. Huber, W. Glockle, H. Kamada, H. Witała, J. Golak
abstract
High precision benchmark calculations for phase shifts and mixing parameters as well as observables in elastic neutron-deuteron scattering below the deuteron breakup threshold are presented using a realistic nucleon-nucleon potential. Two totally different methods, one using a variational principle in configuration space and the other solving the Faddeev equations in momentum space, are used and compared to each other. The agreement achieved in phase shifts and mixing parameters as well as in the polarization observables is excellent. The extreme sensitivity of the vector analyzing power A(gamma) to small changes of the phase shifts and mixing parameters is pointed out. [S0556-2813(98)07312-9].
The hypertriton and its decays
W. Glockle, K. Miyagawa, H. Kamada, J. Golak, H. Witała
abstract
Rigorous Faddeev calculations for the hypertriton, based on modern baryon-baryon forces including Lambda-Sigma conversion, are described. The mesonic and nonmesonic decay modes are evaluated taking the final-state interaction among the three nucleons exactly into account. Total and differential decay rates are provided. It is shown that the total rates for neutron- and proton-induced decays in the nonmesonic mode cannot be seperated experimentally, only fractions thereof.
Cross section minima in elastic Nd scattering: Possible evidence for three-nucleon force effects
H. Witała, W. Glockle, D. Huber, J. Golak, H. Kamada
abstract
Neutron-deuteron elastic scattering cross sections are calculated at different energies using modern nucleon-nucleon (NN) interactions and the Tucson-Melbourne three-nucleon force adjusted to the triton binding energy. Predictions based on NN forces only underestimate nucleon-deuteron data in the minima at higher energies starting around 60 MeV. Adding the three-nucleon forces fills up those minima and reduces the discrepancies significantly. [S0031-9007(98)06806-9].
Inadequacies of the nonrelativistic 3N Hamiltonian in describing the n+d total cross section
WP. Abfalterer, FB. Bateman, FS. Dietrich, C. Elster, RW. Finlay, W. Glockle, J. Golak, RC. Haight, D. Huber, GL. Morgan, H. Witała
abstract
New high-precision measurements of the neutron total cross section for hydrogen and the deuterium-hydrogen cross section difference were pel formed for neutron energies between 7 and 600 MeV. The results are compared with state-of-the-art Faddeev calculations of the neutron-deuterium system up to 300 MeV. Above 100 MeV, this comparison reveals significant limitations of the nonrelativistic 3N Hamiltonian using nucleon-nucleon forces only.
Tensor analyzing power A(yy) of (d)over-right-arrow-p radiative capture
H. Anklin, LJ. de Bever, S. Buttazzoni, W. Glockle, J. Golak, A. Honegger, J. Jourdan, H. Kamada, G. Kubon, T. Petitjean, LM. Qin, I. Sick, P. Steiner, H. Witała, M. Zeier, J. Zhao, B. Zihlmann
abstract
Proton-deuteron radiative capture has been studied with polarized deuterons at a laboratory deuteron energy E-d = 45 MeV. Precise data for the tensor analyzing power A(yy) have been measured in the angular range 50 degrees to 160 degrees. Three-nucleon Faddeev wave functions in the initial scattering and final bound state are calculated using realistic nucleon-nucleon potentials. Mesonic exchange currents are included according to Siegert's theorem. Comparison to other recent experimental data is performed as well. (C) 1998 Elsevier Science B.V.
Elastic pd scattering with 200-300 MeV protons
H. Rohdjess, W. Scobel, HO. Meyer, PV. Pancella, SF. Pate, MA. Pickar, RE. Pollock, B. Von Przewoski, T. Rinckel, F. Sperisen, H. Witała, J. Golak, D. Huber, H. Kamada, W. Glockle
abstract
We have measured the pd elastic scattering with an electron-cooled beam of a proton storage ring and an internal jet target operated with HD gas. The accurately known H/D ratio is used to transfer the precision of existing pp scattering data to the pd cross sections. Measurements were performed for proton energies be tween 200 and 300 MeV in the angular range 11 degrees less than or equal to Theta(c.m.) less than or equal to 29 degrees. The results are compared to nonrelativistic Faddeev calculations with different nucleon-nucleon interactions and total angular momenta j less than or equal to 5 in the NN subsystem. The impact of a genuine 3N force is investigated. The discrepancies between data and calculations increase with projectile energy. [S0556-2813(98)04805-5].
pi-mesonic decay of the hypertriton
H. Kamada, J. Golak, K. Miyagawa, H. Witała, W. Glockle
abstract
The pi-mesonic decay of the hypertriton is calculated based on a hypertriton wave function and 3N scattering states, which are rigorous solutions of three-body Faddeev equations using realistic NN and hyperon-nucleon interactions. The total pi-mesonic decay rate is found to be 101% of the free Lambda decay rate, which is close to the experimental data. Together with the nonmesonic decay the total lifetime of H-3(Lambda) is predicted to be 2.56 x 10(-10) sec which is 3% smaller than for the free Lambda particle. The differential decay rate is evaluated as a function of the pion momentum. The decay into the N + d + pi channel is stronger than in the 3N + pi channel in contrast to the situation for the nonmesonic decay. The ratio for the decay rate into He-3 + pi(-) to the decay rate into all channels including pi(-) is found to be 0.379, which is close to the experimental value. We visualize the decay into the dominant channel p + d + pi(-) in a Dalitz plot. Finally we compare the polarization of the outgoing proton in free unpolarized Lambda decay to the polarization of He-3 in unpolarized, H-3(Lambda) decay and we compare the closely related asymmetry of pi(-) emitted parallel and antiparallel with respect to the spin direction for a polarized Lambda to the corresponding asymmetry for a polarized H-3(Lambda). [S0556-2813(98)01104-2].
Pion absorption reaction on H-2 and He-3 in the Delta-isobar region
H. Kamada, MP. Locher, TSH. Lee, J. Golak, VE. Markushin, W. Glockle, H. Witała
abstract
By using Faddeev equations the absorption of pi(+) on He-3 in the Delta-isobar region is investigated with the final state three-nucleon interaction. We calculated the NN-NDelta t-matrix and piNDelta-right-arrow-Delta vertex from a phenomenological model for NN and pid reactions. In case of neglecting the initial pion scattering effects the theoretically predicted peaks of the pion absorption cross sections for H-2 and He-3 occur at too high an energy with respect to the data. It is shown that the final state three-nucleon interactions have a negligible effect on the magnitude and the shift of the peak position. By a small modification of the Delta bare mass and the piNDelta coupling strength the peak positions of the absorption cross sections of H-2 and He-3 are simultaneously brought to the correct peak position. The Dalitz plots of the outgoing three protons are shown and compared to the recent PSI measurements using kinematics cuts which almost eliminate the contribution from quasi free pion absorption.
Proton induced deuteron breakup reaction at 65 MeV: Unspecific configurations
K. Bodek, W. Glockle, J. Golak, L. Jarczyk, S. Kistryn, B. Kozlowska, J. Lang, A. Micherdzinska, O. Naviliat-Cuncic, J. Smyrski, M. Sokolowski, J. Sromicki, A. Strzalkowski, H. Witała, J. Zejma, W. Zipper
abstract
The nonmesonic weak decay of the hypertriton
J. Golak, K. Miyagawa, H. Kamada, H. Witała, W. Glockle, A. Parreno, A. Ramos, C. Bennhold
abstract
The nonmesonic decay of the hypertriton is calculated based on a hypertriton wavefunction and 3N scattering states, which are rigorous solutions of 5-body Faddeev equations using realistic NN and hyperon-nucleon interactions. The pion-exchange together with heavier meson exchanges for the Lambda N --> NN transition is considered. The total nonmesonic decay rate is found to be 1.7% of the free Lambda decay rate. Integrated as well as differential decay rates are given. The p- and n-induced decays are discussed thoroughly and it is shown that the corresponding total rates cannot be measured individually.
Proton induced deuteron breakup reaction at 65 MeV: Unspecific configurations
K. Bodek, W. Glockle, J. Golak, L. Jarczyk, S. Kistryn, B. Kozlowska, J. Lang, A. Micherdzinska, O. Naviliat-Cuncic, J. Smyrski, M. Sokolowski, J. Sromicki, A. Strzalkowski, H. Witala, J. Zejma, W. Zipper
abstract
Inclusive scattering of polarized electrons on polarized He-3: Effects of final state interaction and the magnetic form factor of the neutron
S. Ishikawa, J. Golak, H. Witała, H. Kamada, W. Glockle, D. Huber
abstract
Effects of final state interaction on asymmetries in inclusive scattering of polarized electrons on polarized He-3 are investigated using a consistent He-3 bound state wave function and 3N continuum scattering states. Significant effects are found, which influence the extraction of the magnetic neutron form factor from A(T'). The enhancement found experimentally for A(TL') near the 3N breakup threshold, which could not be explained in calculations carried through in plane wave impulse approximation up to now, occurs now also in theory if the full final state interaction is included.
Three-nucleon scattering: Numerical challenges and physical insights
W. Glockle, H. Witała, D. Huber, H. Kamada, J. Golak
abstract
The numerical solution of three-nucleon (3N) Faddeev equations is sketched. Successes and failures in the description of 3N scattering data are illustrated in examples. Measurements are proposed which appear promising to see 3N force (3NF) effects based on a 3NF model, which is adjusted to the H-3 binding energy.
Nonmesonic weak decay of the hypertriton (vol 55, pg 2196, 1997)
J. Golak, K. Miyagawa, H. Kamada, H. Witała, W. Glockle, A. Parreno, A. Ramos, C. Bennhold
abstract
Optical nucleon-deuteron potential
J. Kuros, H. Witała, W. Glockle, J. Golak, D. Huber, H. Kamada
abstract
Nucleon-deuteron scattering is cast into the form of an optical potential formalism. Two forms of an optical potential are given. The resulting integral equations for the optical potentials are approximated by the first two leading terms. Our numerical results demonstrate that even at intermediate energies these approximations are insufficient to cover all of the angular range. Rescattering terms of higher order in the nucleon-nucleon (NN) t matrix are needed. If one focuses on forward scattering, low-order approximations in the NN t matrix can be sufficient, depending on energy, and observable.
Nonmesonic weak decay of the hypertriton
J. Golak, K. Miyagawa, H. Kamada, H. Witała, W. Glockle, A. Parreno, A. Ramos, C. Bennhold
abstract
The nonmesonic decay of the hypertriton is calculated based on a hypertriton wave function and 3N scattering states, which are rigorous solutions of three-body Faddeev equations using realistic NN and hyperon-nucleon interactions. The pion exchange together with heavier meson exchanges for the Lambda N-->NN transition is considered. The total nonmesonic decay rate is found to be 0.5% of the free Lambda decay rate. Integrated as well as differential decay rates are given. The p- and n-induced decays are discussed thoroughly and it is shown that the corresponding total rates cannot be measured individually.
Pion absorption cross section for H-2 and He-3 in the Delta-isobar region: A phenomenological connection
H. Kamada, MP. Locher, TSH. Lee, J. Golak, VE. Markushin, W. Glockle, H. Witała
abstract
The absorption of pi(+) on He-3 in the Delta region is evaluated with exact inclusion of the final state interaction among the three emerging protons. The absorption is described by a pi N --> Delta vertex and an N Delta-NN transition t matrix which are calculated from a phenomenological model for NN and pi d reactions. In a calculation where the initial pion scattering effects are neglected, the predicted peaks of the pion absorption cross sections for H-2 and He-3 lie too high in energy in relation to the data. The effect of the final-state three-nucleon interaction turns out to be too small for changing the magnitude and shifting the peak position of the total absorption cross section for He-3. We demonstrate that the adjustment of the peak position for the deuteron cross section by small modifications of the Delta parameters automatically leads to the correct peak position in He-3.
Cross sections and analysing powers A(y) in the breakup reaction H-2((p)over-right-arrow,pp)n at 65 MeV: Star configurations
J. Zejma, M. Allet, K. Bodek, J. Lang, R. Muller, S. Navert, O. NaviliatCuncic, J. Sromicki, E. Stephan, L. Jarczyk, S. Kistryn, J. Smyrski, A. Strzalkowski, W. Glockle, J. Golak, D. Huber, H. Witała, PA. Schmelzbach
abstract
Cross-section and vector-analyzing-power data for three star configurations of the H-2((p) over right arrow,pp)n breakup reaction at E(p)(lab)=65 MeV were measured in a kinematically complete experiment. They are compared to rigorous Faddeev calculations involving five realistic charge-dependent nucleon-nucleon potentials: Argonne v(18), CD Bonn, Nijmegen 93, Nijmegen I, and Nijmegen II. A general satisfactory agreement between theory and experiment has been found. However, there exist also a few minor discrepancies in cross sections in some regions of phase space. The experimental data are compared also to the calculations including the (pi-pi) Tucson-Melbourne three-body force. Their effects are either negligible or increase the disagreement with the experiment.
Pion absorption on He-3
H. Kamada, MP. Locher, TSH. Lee, W. Glockle, H. Witała, J. Golak
abstract
Pion absorption in the pi(+) He-3 --> ppp reaction is investigated using the Faddeev formalism. As preliminary results, the differential cross sections for the two- and three-body absorption mechanics are shown.
Measurement of the longitudinal analyzing power for noncoplanar p-d breakup
EA. George, J. Frandy, MK. Smith, Y. Zhou, LD. Knutson, J. Golak, H. Witała, W. Glockle, D. Huber
abstract
First measurements of the longitudinal analyzing power A(z) for noncoplanar p-d breakup at E(p) = 9 MeV in four kinematically complete configurations are presented. The measurements are compared with Faddeev calculations obtained with the Bonn B nucleon-nucleon interaction and the 2 pi-exchange Tucson-Melbourne three-nucleon force. The measured analyzing powers and the corresponding theoretical predictions are very small in magnitude and compatible within the error bars of the data. Because of the smallness of A(z), the expected enhanced sensitivity to three-nucleon force effects is not seen in this: low energy region.
Cross-section measurements for the H-2(g,n)2p reaction at 135 MeV
BD. Anderson, AR. Baldwin, W. Bertozzi, TN. Buti, A. Fazely, JM. Finn, CC. Foster, W. Glockle, J. Golak, MA. Kovash, R. Kurmanov, R. Madey, B. Murdoch, PC. Tandy, JW. Watson, H. Witała
abstract
Cross-section excitation-energy spectra and angular distributions were measured for the H-2(p,n)2p reaction at 135 MeV in 6 degrees steps from 0 degrees to 30 degrees (laboratory), using the beam swinger facility at the Indiana University Cyclotron Facility. The target was a 12.8 mg/cm(2) foil of CD2. Neutron energies were measured by the One-of-flight method using large-volume plastic scintillator arrays at flight paths of 91 m. The overall energy resolution was 260 keV. The 0 degrees spectrum is dominated by a large peak near 0 MeV of relative energy in the final 2p system; this peak corresponds to the two protons. in the S-1(0) state. The wider-angle spectra are dominated by a broad peak centered at 10 to 20 MeV of excitation which is the quasifree scattering peak. The spectra are compared with impulse approximation and three-body Faddeev calculations.
The three-nucleon continuum: Achievements, challenges and applications
W. Glockle, H. Witała, D. Huber, H. Kamada, J. Golak
abstract
After a brief historic overview the basic equations for three-nucleon (3N) scattering based on general two-nucleon and 3N forces are reviewed and the main steps for their derivation are given. Also the expressions for the various observables, elastic and breakup cross sections, as well as the great variety of spin observables are displayed and derived. The treatment of the 3N Faddeev equations in momentum space and in a partial wave decomposition is outlaid in some detail, the handling of the singularities in the integral kernel described and the algorithms and techniques used to solve the large set of equations in the discretized form are presented. Accuracy tests in form of benchmark calculations, where our results are compared to the ones of other techniques, are given. The bulk part of this review, however, is devoted to the comparison of very many observables in elastic nucleon-deuteron (Nd) scattering and the breakup process to the predictions based on the most modern nucleon-nucleon (NN) forces AV18, Nijmegen93, Nijmegen I and II and a recently updated OBE-potential CD Bonn. Overall the agreement with the data is excellent and there is little room left for the action of a three-nucleon force (3NF). The effects of the pi-pi, pi-rho and rho-rho exchange 3NF's of the Tucson-Melbourne model are studied. They are in general small and in the few cases where discrepancies to data occur using NN forces only, they go into the wrong direction. We propose quite a few measurements, which should help to get more information on the potential energy of three nucleons. Several special topics are discussed: Do certain 3N scattering observables scale with the triton binding energy? Which of the 3N breakup cross sections are totally insensitive to the choice of the NN force and which are very sensitive? How well can one extract the nn scattering length from the 3N breakup? We discuss the outsticking discrepancy of the 3N analyzing power A(y) in low energy elastic Nd scattering; the eigen phase shifts and mixing parameters in elastic nd scattering; the simplifications of 3N scattering at high energies and the formulation of the optical potential for elastic nd scattering and its limiting form at high energies. Alternative approaches to solve 3N scattering: in configuration space, using finite rank expansions of NN forces, variational techniques and the hybrid Sendai method are briefly described as well as the proton proton Coulomb force problem in the pd system and the question how to incorporate relativity. Finally some applications are sketched where a 3N final state occurs and where the interaction among the nucleons requires a correct treatment. We mention inelastic electron scattering as well as pi-absorption on He-3 (H-3) and nonmesonic decay of the hypertriton.
Low energy proton-deuteron versus neutron-deuteron breakup in four configurations: Implications for Coulomb-force effects
R. Grossmann, G. Nitzsche, H. Patberg, L. Sydow, S. Vohl, HPG. Schieck, J. Golak, H. Witała, W. Glockle, D. Huber
abstract
We have measured cross sections of the pd breakup reaction at a laboratory proton energy of 10.5 MeV in four kinematically complete arrangements comprising space-star, collinearity, final-state interaction and quasi-free scattering conditions, We present our results and compare them to the predictions of rigorous three-nucleon Faddeev calculations using different realistic nucleon-nucleon potentials, We find cases of good agreement but also cases of clear discrepancies. The inclusion of the 2 pi-exchange Tucson-Melbourne three-nucleon force does not remove these discrepancies. Considering also pd data at 13 and 19 MeV and nd data at 10.5 and 13 MeV, we draw tentative conclusions about possible Coulomb-force effects in these configurations, In the quasi-free scattering, space-star, and collinear configurations, the Coulomb-force effects might possibly be responsible for at least part of the observed discrepancies, For the np FSI configuration the Coulomb-force effects are likely to be small.
Effects of the Tucson-Melbourne three-nucleon force in the proton-deuteron breakup process at E(p)=65 MeV
M. Allet, K. Bodek, J. Golak, W. Glockle, W. Hajdas, D. Huber, L. Jarczyk, H. Kamada, S. Kistryn, J. Lang, R. Muller, O. NaviliatCuncic, J. Smyrski, J. Sromicki, A. Strzalkowski, H. Witała, J. Zejma
abstract
We present the calculated cross sections and vector analyzing powers using the Bonn B nucleon-nucleon potential and the Tucson-Melbourne three-nucleon force (3NF) for six collinearity and quasi-free scattering breakup configurations. These calculations are compared to the results of the recent kinematically complete pd experiments at E(p) = 65 MeV. The Tucson-Melbourne 3NF, adjusted together with the Bonn B potential to reproduce the triton binding energy, leads to small effects both in cross sections and analyzing powers in all six studied configurations.
Deuteron breakup reaction H-2((p)over-right-arrow,pp)n induced by polarized protons at E(p)=19.0 MeV
H. Patberg, R. Grossmann, G. Nitzsche, L. Sydow, S. Vohl, HPG. Schieck, J. Golak, H. Witała, W. Glockle, D. Huber
abstract
We measured cross sections and vector analyzing powers of the breakup reaction H-2((P) over right arrow,pp)n at a laboratory proton energy of 19.0 MeV in four kinematically complete arrangements comprising space star, collinearity, final-state interaction, and quasifree scattering conditions. We present our results and compare them to the predictions of rigorous three-nucleon Faddeev calculations using different realistic nucleon-nucleon potentials. We found cases of good agreement but also cases of clear discrepancies. The inclusion of the 2 pi-exchange Tucson-Melbourne three-nucleon force does not remove these discrepancies but even worsens the description in all cases. In the quasifree scattering and space star configurations Coulomb-force effects might possibly be responsible for at least part of the observed discrepancies.
Proton-induced deuteron breakup at E(p)(lab)=65 MeV in quasi-free scattering configurations
M. Allet, K. Bodek, W. Hajdas, J. Lang, R. Muller, S. Navert, O. NaviliatCuncic, J. Sromicki, J. Zejma, L. Jarczyk, S. Kistryn, J. Smyrski, A. Strzalkowski, H. Witała, W. Glockle, J. Golak, D. Huber, H. Kamada
abstract
The proton-deuteron breakup cross sections and analyzing powers A(y) for three kinematically complete configurations in a quasi-free-scattering geometry have been measured at E(p)(lab) = 65 MeV. The data are compared with predictions of rigorous Faddeev calculations using the Argonne AV14, Bonn-B, Nijmegen-78, and Paris potentials. A satisfactory agreement between theory and experimental data, both for cross sections and analyzing powers, has been found.
Nuclear three- and four-body systems
W. Glockle, H. Kamada, H. Witała, D. Huber, J. Golak, K. Miyagawa, S. Ishikawa
abstract
Cross sections and vector analyzing powers in the proton induced deuteron breakup reaction at 65 MeV: Star configurations
M. Allet, K. Bodek, W. Glockle, J. Golak, L. Jarczyk, S. Kistryn, J. Lang, R. Muller, S. Navert, O. NaviliatCouncic, J. Smyrski, J. Sromicki, E. Stephan, A. Strzalkowski, H. Witała, J. Zejma
abstract
Achievements and challenges in 3N- and 4N-systems
W. Glockle, H. Witała, H. Kamada, D. Huber, J. Golak
abstract
S-matrix parameters for elastic neutron-deuteron scattering above the breakup threshold
D. Huber, J. Golak, H. Witała, W. Glockle, H. Kamada
abstract
Cross sections and vector analyzing powers in the proton induced deuteron breakup reaction at 65 MeV: Star configurations
M. Allet, K. Bodek, W. Glockle, J. Golak, L. Jarczyk, S. Kistryn, J. Lang, R. Muller, S. Navert, O. NaviliatCouncic, J. Smyrski, J. Sromicki, E. Stephan, A. Strzalkowski, H. Witala, J. Zejma
abstract
Proton-induced deuteron breakup at E(p)(lab)=65 MeV in quasi-free scattering configurations
M. Allet, K. Bodek, W. Hajdas, J. Lang, R. Muller, S. Navert, O. NaviliatCuncic, J. Sromicki, J. Zejma, L. Jarczyk, S. Kistryn, J. Smyrski, A. Strzalkowski, H. Witala, W. Glockle, J. Golak, D. Huber, H. Kamada
abstract
The proton-deuteron breakup cross sections and analyzing powers A(y) for three kinematically complete configurations in a quasi-free-scattering geometry have been measured at E(p)(lab) = 65 MeV. The data are compared with predictions of rigorous Faddeev calculations using the Argonne AV14, Bonn-B, Nijmegen-78, and Paris potentials. A satisfactory agreement between theory and experimental data, both for cross sections and analyzing powers, has been found.
Tensor analyzing power A(yy) for dp breakup in the symmetric constant relative energy configuration
H. Witała, J. Golak, W. Glockle, D. Huber, H. Kamada, W. Tornow, EJ. Stephenson, DA. Low
abstract
The tensor analyzing power A(yy) in the symmetric constant relative energy geometry for the dp breakup reaction has been calculated using solutions of the three-nucleon Faddeev equations based on the Argonne AV14, AV18, Bonn-B, Nijm78, Nijm93, NijmI, NijmII, and Paris potentials, as well as the Bonn-B potential in conjunction with the Tucson-Melbourne three-nucleon interaction. The comparison with recent dp data at E(d)=94.5 MeV revealed a clear discrepancy in the region where the data exhibit a pronounced structure which is not present in the theoretical results.
Phase shifts and mixing parameters for elastic neutron-deuteron scattering above breakup threshold
D. Huber, J. Golak, H. Witała, W. Glockle, H. Kamada
abstract
Complex eigenphases and mixing parameters for elastic n-d scattering above the breakup threshold are calculated. Faddeev equations are solved precisely using the Bonn-B NN potential. We point out defects in existing N-d phase-shift analyses. Peculiar energy variations in the mixing parameter eta(3/2-) are shown to have no effect on observables and are simply an artifact of the S-matrix parametrization. It is shown, that the n-d analyzing power A(y) depends most sensitively on the three eigenphases delta(3/2,1)(1/2), delta(3/2,1)(3/2), and delta(3/2,1)(5/2), which again are predominantly generated by the P-3(j) NN force components. Therefore a determination of those eigenphases from experimental data would help to constrain the P-3(j) NN forces.
