ON THE SEPARATION METHOD FOR THE NUCLEAR MANY-BODY PROBLEM

Abstract

A method of calculation of the nuclear reaction matrix is proposed in which the interaction is divided into two parts. The long-range part of the interaction together with the kinetic energy forms the unperturbed Hamiltonian and the short-range interaction is treated as a perturbation. The separation distance is so chosen that the perturbation produces no energy shift, but modifies the many-body wave function. For the special case where the outer part of the interaction is sufficiently weak, a plane-wave approximation is used for the unperturbed wave function, with the result that the diagonal elements of the reaction matrix are given by the first Born approximation of the long-range part of the potential. An iteration scheme is set up to compute the dividing point of the interaction. Such properties of nuclear matter as saturation, binding energy, and rearrangement energy are discussed in terms of the separation distance and its derivatives. Finally, this method is compared with those of Moszkowski and Scott (1960) and Bethe et al. (1963).