Towards an extended microscopic theory for upper-fp-shell nuclei

An extended SU(3) shell model that for the first time explicitly includes particles from the unique-parity levels in nuclei is introduced. Its relevance is established through calculations performed with realistic interactions for a group of upper fp-shell isotopes 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. Specifically, the outcome suggests that the pseudo-SU(3) symmetry is quite good throughout the region and that only part of the configurations are relevant for the structure of the low-lying states. 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. More detailed analyses of the extended SU(3) model are done for two nuclei of special interest in astrophysics, namely the waiting-point nuclei $^{64}$Ge and $^{68}$Se. The strengths and limitations of the theory are demonstrated by its ability to describe various nuclear characteristics. Specifically, energy spectra, B(E2) transition strengths and wave-function content are compared with the realistic results. In addition, the dominance of configurations with different distribution of particles and the role that several newly-introduced terms play in the Hamiltonian are investigated. The extended SU(3) approach allows one to better probe the effects of deformation and account for these key properties of the system within a highly-truncated model space. The model also promises to be useful for nuclei from the rare-earth and actinide regions. Specifically, by ensuring a robust number of collective degrees of freedom and Hamiltonians with a larger number of degrees of freedom, it should allow one to give a satisfactory explanation of the experimentally-observed existence of an abundance of low-lying $0^{+}$ states and very strongly enhanced B(E2) strengths found in these nuclei. This version of the theory will extend previous results from the pseudo-SU(3) model where the role of nucleons in the intruder levels was relegated to a very simple renormalization of the dynamics defined by nucleons in the normal-parity spaces only