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

TL;DR

This paper introduces an extended SU(3) shell model that explicitly includes unique-parity levels, improving the understanding of deformation and properties of upper fp-shell nuclei like $^{64}$Ge and $^{68}$Se.

Contribution

The paper presents the first explicit inclusion of unique-parity levels in an extended SU(3) shell model for upper fp-shell nuclei.

Findings

Enhanced ability to probe deformation effects.

Accurate accounting of key nuclear properties.

Effective use of a highly truncated model space.

Abstract

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 ($f_{5/2},p_{3/2},p_{1/2}$) and the unique parity $g_{9/2}$ 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 $g_{9/2}$ 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.