The binding energies of atomic nuclei I. Introduction and general method

Abstract

The energy of an atomic nucleus can be written as an expansion in terms of an effective two-nucleon interaction and a trial single-particle potential. The effective interaction can be derived from a phenomenological internucleon potential using a suitable extension of the methods of Brueckner for infinite nuclear matter. Coupled integro-differential equations are obtained for the relative wave functions of pairs of nucleons. These are simplified by using a harmonic oscillator potential to give the one-particle wave functions and by approxi­mating the effects of the exclusion principle. A further modification of the method leads to a generalized perturbation procedure in which the more complicated parts of the inter­-nucleon potential occur only in differential equations. A preliminary study is made of various methods for determining the matrix elements of the effective interaction and the relative wave functions.