H. Witała

The Three nucleon continuum: Achievements, challenges and applications

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 π-π, π-ϱ and ϱ-ϱ exchange 3NFs 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 Ay 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 π-absorption on 3He (3H) and nonmesonic decay of the hypertriton.

Cross Section Minima in Elastic Nd Scattering: Possible Evidence for Three-Nucleon Force Effects

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 60thinspMeV. Adding the three-nucleon forces fills up those minima and reduces the discrepancies significantly. {copyright} {ital 1998} {ital The American Physical Society}

Systematic study of three-nucleon force effects in the cross section of the deuteron-proton breakup at 130 MeV

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 (3NFs) 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 3NFs 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.

Nd elastic scattering as a tool to probe properties of 3N forces

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 are in conflict with data and thus very likely point to defects in those three-nucleon force models.

New Measurement of the {sup 1}S {sub 0} Neutron-Neutron Scattering Length Using the Neutron-Proton Scattering Length as a Standard

The present paper reports high-accuracy cross-section data for the 2 H(n,nnp) reaction in the neutron-proton (np) and neutron-neutron (nn) final-state-interaction (FSI) regions at an incident mean neutron energy of 13.0 MeV. These data were analyzed with rigorous three-nucleon calculations to determine the 1 S0 np and nn scattering lengths, anp and ann. Our results are ann = -18.7±0.6 fm and anp = -23.5 ±0.8 fm. Since our value for anp obtained from neutron-deuteron (nd) breakup agrees with that from free np scattering, we conclude that our investigation of the nn FSI done simultaneously and under identical conditions gives the correct value for ann. Our value for ann is in agreement with that obtained in � − d measurements but disagrees with values obtained from earlier nd breakup studies.

Systematic investigation of the elastic proton-deuteron differential cross section at intermediate energies

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 .

The neutron charge form factor and target analyzing powers from 3He(e→,e′n) scattering

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.

Three- and Four-Nucleon Systems from Chiral Effective Field Theory

Recently developed chiral nucleon-nucleon (NN) forces at next-to-leading order (NLO), that describe NN phase shifts up to about 100 MeV fairly well, have been applied to 3N and 4N systems. Faddeev-Yakubovsky equations have been solved rigorously. The resulting 3N and 4N binding energies are in the same range as found using standard NN potentials. In addition, low-energy 3N scattering observables are very well reproduced as for standard NN forces. The long-standing A(y) puzzle is absent at NLO. The cutoff dependence of the scattering observables is rather weak.

Few-nucleon systems with state-of-the-art chiral nucleon-nucleon forces

eld theory, along with a new analysis of the theoretical truncation errors, to study nucleon-deuteron (Nd) scattering and selected low-energy observables in 3 H, 4 He, and 6 Li. Calculations beyond second order dier from experiment well outside the range of quantied 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 eects and estimate the achievable accuracy of theoretical predictions for various observables.

Evidence for a Three-Nucleon-Force Effect in Proton-Deuteron Elastic Scattering

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(y), iT11, and C(y,y) 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.