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 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 π-absorption on 3He ( 3H) and nonmesonic decay of the hypertriton.