Rigorous Faddeev Calculations Research Articles

FEW-NUCLEON STUDIES AT INTERMEDIATE ENERGIES

Observables in proton-deuteron scattering are sensitive probes of the nucleon-nucleon interaction and three-nucleon force effects. Several facilities, including the KVI, allow a detailed study of few-nucleon interactions below the pion-production threshold exploiting polarized proton and deuteron beams. In this contribution, some recent results are discussed and interpreted exploiting rigorous Faddeev calculations. Furthermore, experimental inconsistencies between two measurements of the cross section in elastic proton-deuteron scattering at 135 MeV/nucleon are reviewed.

Three-body dN interaction in the analysis of the 12C[formula omitted] reaction at 270 MeV

We have measured the cross sections and analyzing powers Ay and Ayy for the elastic and inelastic scattering of deuterons from the 0+(g.s.), 2+(4.44 MeV), 3−(9.64 MeV), 1+(12.71 MeV), and 2−(18.3 MeV) states in 12C at an incident energy of 270 MeV. The data are compared with microscopic distorted-wave impulse approximation calculations where the projectile-nucleon effective interaction is taken from the three-nucleon t-matrix given by rigorous Faddeev calculations presently available at intermediate energies. The agreement between theory and data compares well with that for the (p,p′) reactions at comparable incident energies/nucleon.

Proton-Induced Deuteron Breakup Reaction at 65 MeV: Unspecific Configurations

Cross sections and vector-analyzing powers for four unspecific configurations of the 2H(p,pp)n breakup reaction at E lab p = 65MeV 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 v 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.

New attempt to determine the n-n scattering length with the 2H(n, np)n reaction

The n-n final-state interaction (FSI) was investigated via the 2H(n, np)n reaction at 25 MeV, using a geometry which enables the simultaneous observation of n-p quasifree (QFS) scattering. The data were analyzed with Monte Carlo simulations based on rigorous Faddeev calculations with realistic nucleon-nucleon potentials. The value of a(nn) deduced from the absolute yield in the FSI peak is -16.27+/-0. 40 fm while the relative data, normalized in the QFS region, give -16.06+/-0.35 fm. Thus our results differ from the "recommended" value of a(nn) = -18.5+/-0.3 fm by more than 5 standard deviations.

Proton induced deuteron breakup reaction at 65 MeV: Unspecific configurations

Cross sections and vector-analyzing powers for four unspecific configurations of the 2H(p,pp)n breakup reaction at Elabp = 65MeV 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 v18, 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.

Cross sections and analyzing powersAyin the breakup reaction2H(p→,pp)nat 65 MeV: Star configurations

Cross-section and vector-analyzing-power data for three star configurations of the ${}^{2}\mathrm{H}(p\ensuremath{\rightarrow},pp)n$ breakup reaction at ${E}_{p}^{\mathrm{lab}}=65$ 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 (\ensuremath{\pi}-\ensuremath{\pi}) Tucson-Melbourne three-body force. Their effects are either negligible or increase the disagreement with the experiment.

Low energy proton-deuteron versus neutron-deuteron breakup in four configurations: implications for Coulomb-force effects

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 2π-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.

Proton-Induced Deuteron Breakup at E lab P = 65 MeV in Quasi-Free Scattering Configurations

The proton-deuteron breakup cross sections and analyzing powers Ay for three kinematically complete configurations in a quasi-free-scattering geometry have been measured at ElabP = 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.

Complete set of deuteron analyzing powers in deuteron-proton elastic scattering: Measurement and realistic potential predictions

Tensor analyzing powersiT11,T20,T21 andT22, have been measured for deuteron laboratory energiesE lab d =75, 85, 95, 106, 119, 131, 144, 156, 172, and 187 MeV. The data are compared to rigorous Faddeev calculations with realistic nucleon-nucleon potentials. A generally good description of the data at all energies is obtained.

Study of the kinematically complete breakup reaction 2H(p̄, pp)n at Ep = 3 Mev with polarized protons

The breakup reaction 2H(p̄, pp)n at E p = 13.0 MeV has been measured in a kinematically complete experiment with polarized protons in four special kinematical situations: np final-state interaction, pp quasi-free scattering, collinearity and symmetric space star. These configurations are identical to those of a corresponding 2H(n, nn) 1H experiment. The cross sections d 3σ/ dΩ 3 dΩ 4 dS and the vector analyzing powers A 1 are presented as a function of the arclenght of the relevant kinematical loci. They are compared to the rigorous Faddeev calculations using realistic meson-exchange NN potentials, i.e. the Paris and Bonn potential. Comparison with the cross section data of the analog neutron experiment is made. In the quasi-free scattering and the space-star cross sections marked discrepancies with the theoretical predictions, in the latter case also with the neutron results are found. In the collinear and final-state interaction situations the agreement is rather good as well as for all analyzing powers and is even improved by taking the finite angular spread into account.

The low-energy neutron-deuteron analyzing power and the 3P 0,1,2 interactions of nucleon-nucleon potentials

Data for the analyzing power A y ( θ) for the elastic scattering of neutrons from deuterons have been measured at 5.0, 6.5 and 8.5 MeV to an accuracy of ±0.0035. Surprisingly large differences have been observed at these low energies between the data and rigorous Faddeev calculations using the Paris and Bonn B nucleon-nucleon potentials. The A y ( θ) data provide a stringent test for our present understanding of the on-shell and off-shell 3P 0,1,2 nucleon-nucleon interactions.

Evidence for three-body forces in p–d breakup at 25 MeV?

Experimental data for deuteron breakup by protons in collinear geometry at 25.00 MeV are compared with the predictions of rigorous Faddeev calculations using the Paris potential and with those of the Doleschall code. The Paris potential significantly underdetermines the breakup cross section in collinear geometry. The explanation for this discrepancy is not entirely clear at this time.

Investigation of the nucleon-nucleon tensor force in the three-nucleon system

Proton-deuteron elastic scattering has been investigated at E p =22.7 MeV by comparison of rigorous Faddeev calculations with experimental results. The observable most sensitive to the tensor force is the nucleon-nucleon polarization transfer coefficient K y y′ . The new angular distribution of K y y′ clearly favours the tensor force of the Bonn A potential, which is weaker than the one of the Paris potential.

Investigation of ϵ1 and the 3PJ phase shifts in the n-p system by the measurement of polarization transfer coefficients in p-d elastic scattering

The 3S 1− 3D 1 mixing parameter ϵ 1 and the 3P J phase shifts in the N-N system at low energy are investigated in the three nucleon system. The sensitivity of polarization transfer coefficients in p-d elastic scattering is determined by rigorous Faddeev calculations using Paris and Bonn potentials. The experimental results of K y y' favours the tensor force component of the Bonn A potential.

Three nucleon scattering — A test for nuclear dynamics

Three nucleon scattering is reviewed with emphasis on recent rigorous Faddeev calculations using meson-theoretical two-nucleon interactions and their comparison with measurements. Recent progress in the Coulomb problem and configuration-space Faddeev equations are discussed.

Differential cross section of the 2H(n, nnp)-reaction at En = 13 MeV

The differential cross section of the nD break-up reaction was investigated at E n = 13 MeV using the Erlangen multidetector neutron facility. Twenty-two different configurations including np final-state interaction, collinearity, coplanar- and space star were measured in a kinematically complete experiment. The results are compared with rigorous Faddeev calculations based on the Paris potential. The discrepancies between data and calculations indicate imperfections in the potential and may be caused by three-particle effects such as wrong off-shell behavior of the potential or an additional three-body force.

Nucleon-induced deuteron breakup: Analysis of 14.1 MeV data by rigorous Faddeev calculations with meson-exchange NN interactions.

Kinematically complete breakup experiments for final-state interaction and collinear configurations have been analyzed by rigorous Faddeev calculations. The two-nucleon Paris potential and a one-boson-exchange parametrization of the new Bonn potential have been used. The treatment of charge-dependent forces in the Faddeev scheme is discussed and a simple (2/3-(1/3 rule is derived. In the collinear configuration a significant discrepancy is found between theoretical and experimental cross sections.

Rigorous Faddeev calculations for elastic neutron-deuteron scattering around 8 MeV c.m. energy

Rigorous Faddeev calculations of the cross sections and analysing powers for elastic nd scattering at E n = 10.0, 12.0, 13.0 and 14.1 MeV were made. As two-nucleon interactions we used the Paris potential and two OBE-parametrizations of the new Bonn potential. The nucleon-nucleon interaction was assumed to act in all partial waves with total angular momentum j⩽2. The influence of higher partial waves ( j = 3) and the charge dependence of the NN interaction in the 1S 0 wave were studied. Definite discrepancies between experiment and theoretical prediction for the neutron analysing powers were found.

Quasi-free scattering in the 3-N continuum

The interaction of a nucleon with the deuteron leading to break-up at the quasi-free scattering (QFS) condition is studied atE lab =12.0, 22.7, 68.0, and 140.0 MeV. Results of rigorous Faddeev calculations and of the impulse approximation (IA) are compared at these energies for bothn-p andp-p QFS in order to study the importance of rescattering terms. For the two-nucleon interaction the Paris potential is used. It is restricted to act in two-body states with total angular momentumj≤2. Also we compare the Faddeev calculations with experimental data for the QFS cross section and analyzing powerA y and find overall agreement. The behaviour of scattering observables turns out to be different forn-p andp-p QFS. Also the energy dependence of rescattering terms is different in the two cases. For all energies studied the IA is not reliable.

A three-nucleon break-up experiment in comparison with a Faddeev calculation

The D(n,nnp) reaction was investigated in a kinematically complete experiment at En=13 MeV using a multidetector set-up. Three of the measured configurations (np FSI, collinearity and space star) were compared with predictions of rigorous Faddeev calculations based on the Paris potential. Differences between theory and experiment are observed for the break-up reaction while the shape of the simultaneously measured elastic cross section is well reproduced.