Schematic Interactions for Nuclear Random-Phase-Approximation Calculations

Abstract

It is customarily believed that schematic interactions are useful for preliminary tests of nuclear models, but are otherwise too unrealistic to be of much value. In this paper, we wish to point out that schematic interactions have a much firmer basis than was supposed, and can therefore be used with more understanding for some of the complex problems, that without simplification are essentially unassailable. An exact criterion is established for the validity of a schematic interaction on the basis of which a new schematic interaction is proposed. This interaction is compared with the surface delta interaction and the $P^{\mathrm{}\left(2\right)\mathrm{}}$ force. On the basis of our criterion, the radial form of the interaction is compared with that suggested for specific excited states, by random-phase-approximation calculations with more general forces. The agreement is favorable.