Nucleon-nucleus scattering and shell model

Abstract

Nucleon-nucleus scattering is treated in a shell model picture, i.e. as in similar investigations the existence of a selfconsistent nuclear single particle potential is assumed representing the dominating part of the nucleon-nucleus interaction. For this case of reasonable splitting into effective one-body and many-body interactions theS-matrix is calculated by the formal methods ofGell-Mann, Goldberger, Watson et al. yielding a factorization into a unitary term which exhibits the potential resonances, times a nuclear structure term containing reduced transition matrix elements. Some approximations are discussed for this matrix of transition probabilities due to residual many-body interactions. In order to test the applicability of the present form for the nucleon-nucleusS-matrix a simplified one-parameter model for this reduced transition matrix is proposed. One application is the analysis of elastic neutron scattering on spherical nuclei in the medium MeV region. Some numerical examples show this form to be comparable with successful optical model calculations. An advantage of the present method is the possibility of determining realistic shell model potentials, especially their nonlocality and other nuclear structure information. In this paper the formalism is used in a rather specific problem, although it is more generally applicable and appears to be a reasonable approximation ot the nuclear scattering problem.