Towards an Extended Microscopic Theory for the Upper fp-shell nuclei

An extended SU(3) shell model that for the first time explicitly includes unique-parity levels is introduced. Shell-model calculations for the isotopes of ${}^{64}$Ge and ${}^{68}$Se are performed where valence nucleons beyond the N=28=Z core occupy levels of the normal parity upper-$fp$ shell ($f_{5\mathrm{/}2},p_{3\mathrm{/}2},p_{1\mathrm{/}2}$) and the unique parity $g_{9\mathrm{/}2}$ intruder configuration. The levels of the upper-$fp$ shell are handled within the framework of an m-scheme basis as well as its pseudo-SU(3) counterpart, and respectively, the $g_{9\mathrm{/}2}$ as a single level and as a member for the complete $gds$ shell. It is demonstrated that the extended SU(3) approach allows one to better probe the effects of deformation and to account for many key properties of the system by using a highly truncated model space.