New effective interaction for $pf$-shell nuclei and its implications for the stability of the $N$=$Z$=28 closed core

The effective interaction GXPF1 for shell-model calculations in the full $pf$ shell is tested in detail from various viewpoints such as binding energies, electro-magnetic moments and transitions, and excitation spectra. The semi-magic structure is successfully described for $N$ or Z=28 nuclei, ${}^{53}$Mn, ${}^{54}$Fe, ${}^{55}$Co and ${}^{56,57,58,59}$Ni, suggesting the existence of significant core-excitations in low-lying non-yrast states as well as in high-spin yrast states. The results of $N=Z$ odd-odd nuclei, ${}^{54}$Co and ${}^{58}$Cu, also confirm the reliability of GXPF1 interaction in the isospin dependent properties. Studies of shape coexistence suggest an advantage of Monte Carlo Shell Model over conventional calculations in cases where full-space calculations still remain too large to be practical.