Shell-Model Calculations with Separable Potentials

Shell-model calculations are performed on ${\mathrm{O}}^{18}$, ${\mathrm{Ca}}^{42}$, ${\mathrm{Zr}}^{90}$, ${\mathrm{Po}}^{210}$, and ${\mathrm{F}}^{18}$ using separable potential forms. In most cases, the potentials have been fitted to low- and intermediate-energy two-body data. The over-all agreement is quite good, and the calculations are considerably simpler than similar ones using hard-core potentials. Replacing the potential matrix by an approximate reaction matrix offers no general improvement and produces results which are comparatively insensitive to the potential parameters.