Perturbation approach to the fermi gas model of heavy nuclei

Abstract

The general perturbation method presented in an earlier paper 1) is applied to a study of some aspects of the Fermi gas model of nuclear matter. The two extreme cases of very low and very high particle density are investigated. It is shown that the theory recently developed by Brueckner 2) can be considered as an improved low density approximation. The validity of some other approximations made in the Brueckner theory, involving the energy denominators in intermediate states are briefly discussed. The study of the case of high density reveals the interesting fact that, contrary to indications presented by Swiatecki 3) and Bethe 4), the convergence of the perturbation expansion gets worse with increasing density, while in that case the Brueckner approximation becomes extremely poor. It is furthermore shown that a slow nucleon, travelling through nuclear matter, can be considered as being in a metastable state and an exact expression for the inverse life-time of such a state is given; this quantity must be identified with the imaginary part of the potential in the optical model.