A nonperturbative study of the isobaric multiplet mass equation

Abstract

An investigation of the isobaric multiplet mass equation (IMME) is carried out, in which the Coulomb interaction is not treated by perturbation theory but is included exactly in a model Hamiltonian. An estimate is made of the leading nonperturbative correction to the usual quadratic IMME, and is compared with results from recent experiments. Two complementary models are developed, in both of which the Coulomb interaction is included exactly. The first is a simple one-particle model which uses a realistic average central nuclear potential, but does not include antisymmetrization effects or residual interactions between valence nucleons. This model allows one to study the A- or Z-dependence of the correction term and determine its order of magnitude. The second model consists of a closed, inert core plus valence nucleons interacting with each other via two-body potentials. This model allows us to study the effect of those features which were ignored in the simple model, but at the cost of introducing the unrealistic harmonic oscillator potential. The results for nuclei of mass number A = 19 confirm the conclusion from the first model that the correction term is of order α rather than Zα, where α is the fine structure constant. Charge dependent effects other than the Coulomb interaction are also studied. It is shown that, in second-order perturbation theory, only the valence nucleons contribute to deviations from the quadratic form of the IMME.