Mixed-Configuration Shell-Model Calculations for Nuclei withN=28,20<Z≤28

Abstract

Level energies, $\gamma$-ray transition rates, and proton spectroscopic factors are calculated for the nuclei with $N=28\mathrm{}$ and $20<Z\le 28$ from simple mixed-configuration shell models. First, the effective-interaction method is used to calculate wave functions in which the pure ($1{f_{\frac{7}{2}}}^n$) configuration and the ($1{f_{\frac{7}{2}}}^{n-1\mathrm{}}2p_{\frac{3}{2}}$) configuration are included. The results are compared with experimental values for 43 levels. The calculated and measured energies and spectroscopic factors agree well, but $M1\mathrm{}$ transition rates are too slow. The model is then extended to include the configuration ($1{f_{\frac{7}{2}}}^{n-1\mathrm{}}1f_{\frac{5}{2}}$). The wave functions are recalculated using additional two-body matrix elements calculated with a modified surface $\delta$ interaction (MSDI) fitted to the effective interactions of the first calculation. The expanded model provides a good fit to energies, spectroscopic factors, and transition rates. For comparison, the calculation is repeated using the reaction matrix elements of Kuo and Brown. The results are less satisfactory than those with the MSDI.