The Elliott SU(3) model in the pf-shell
The "quasi SU(3)" symmetry, uncovered in realistic shell-model calculations in the pf-shell, describes the fact that in the case of well-deformed nuclei the quadrupole-quadrupole and spin-orbit interactions play a dominant role and pairing can be included as a perturbation. In terms of a SU(3) basis, it is shown that the ground state band is built from the S = 0 leading irrep which couples strongly to the leading S = 1 irreps in the proton and neutron subspaces. Furthermore, the quadrupole-quadrupole interaction was found to give dominant weights to the so-called "stretched" coupled representations, which supports a strong SU(3)-dictated truncation of the model space. Using this type of truncation scheme, we studied 48Cr, which has a excitation spectrum like that of a quantum rotor. The Hamiltonian that was used in the study includes a single-particle term as well as pairing and quadrupole-quadrupole interactions. All of the interaction strengths were fixed from systematics. The yrast band energies were well-reproduced up to the backbending regime. By extending this approach it should be possible to perform realistic shell-model calculations for deformed nuclei throughout the periodic table.