Investigation of the effective interaction by means of a modified shell model

Abstract

The effective InteractionU for a shell model with hamiltonianH _m is investigated by means of a “mixed” model with hamiltonianH _m . For this model the Bornv. Neumann expansion of the effective interactionŨ reduces to its first two terms. Within the finite dimensional function space ℜ _n used in the shell model calculation the operatorsU andŨ are exactly equivalent. This is used to show that an energy independent approximation forU- if it is possible at all-is necessarily equal to the residual interaction, i.e. to the difference between nucleon-nucleon interaction and shell model interaction.