Central and tensor potentials in nuclear shell model calculations

Abstract

We present here the results of an attempt to determine an effective interaction for nuclear shell-model problems. A residual interaction with gaussian shape and both central and tensor parts was assumed. The ranges of these parts were fixed, but the strengths of the various spin-parity components were varied to obtain a good fit to a number of nuclear levels. The levels chosen for this fit were those in nuclei which consist of two particles or holes relative to the following closed shell cores: ¹⁶O, ⁴⁰Ca, ⁸⁸Sr, ²⁰⁸Pb. The attempt failed, in that no reasonable set of potential parameters could be found which worked reasonably well for all cases. The greatest success was obtained for those nuclei which have ²⁰⁸Pb as the core, although one of the worst cases of disagreement was ²⁰⁶Tl.