Quasi-SU(3) truncation scheme for even–even sd-shell nuclei

The quasi-SU(3) symmetry was uncovered in full pf and sdg shell-model calculations for both even–even and odd–even nuclei. It manifests itself through a dominance of single-particle and quadrupole–quadrupole terms in a Hamiltonian used to describe well-deformed nuclei. A practical consequence of the quasi-SU(3) symmetry is an efficient basis truncation scheme. In C.E. Vargas et al., Phys. Rev. C 58 (1998) 1488] it is shown that when this type of Hamiltonian is diagonalized in an SU(3) basis, only a few irreducible representations (irreps) of SU(3) are needed to describe the yrast band, the leading S=0 irrep augmented with the leading S=1 irreps in the proton and neutron subspaces. In the present article the quasi-SU(3) truncation scheme is used, in conjunction with a “realistic but schematic” Hamiltonian that includes the most important multipole terms, to describe the energy spectra and B(E2) transition strengths of ^20,22Ne, ²⁴Mg and ²⁸Si. The effect of the size of the Hilbert space on both sets of observables is discussed, as well as the structure of the yrast band and the importance of the various terms in the Hamiltonian. The limitations of the model are explicitly discussed.