Spectroscopy in the Nuclear1f72Shell

Abstract

The intent of the work reported here has been to ascertain which properties of nuclei with $20\le Z$, $N\le 28$ are consistent with wave functions composed of a ${\mathrm{Ca}}^{40}$ core plus $Z-20\mathrm{}$ protons and $N-20\mathrm{}$ neutrons in the $1f_{\frac{7}{2}}$ shell. We have attempted to determine the $1f_{\frac{7}{2}}$ nucleon-nucleon interaction from the observed levels of ${\mathrm{Sc}}^{42}$, assuming that these can be interpreted as due to the configuration ${\left(1\mathrm{}{f}_{\frac{7}{2}}\right)}^2$. Following Talmi, we have then treated this interaction exactly, within the framework of our pure configuration assumption. We have found that many of the observed properties of these nuclei are reproduced by this model, in particular the systematics of low-lying nuclear spins, magnetic moments, $\mathrm{ft}$ values, and ($p, d$) and ($d, p$) spectroscopic factors. However, several nuclei have more low-lying states than the ${\left(1\mathrm{}{f}_{\frac{7}{2}}\right)}^n$ configuration can provide at the corresponding energies.