Investigation of the effective interaction by means of a modified shell model
The effective InteractionU for a shell model with hamiltonianHm is investigated by means of a “mixed” model with hamiltonianHm. For this model the Bornv. Neumann expansion of the effective interactionŨ reduces to its first two terms. Within the finite dimensional function space ℜn 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.