Shape coexistence and superdeformation in 28Si

Abstract

In this Master thesis I analyze the 28Si nucleus within the nuclear shell model using state-of-the-art numerical diagonalizations complemented with the generatorcoordinate method (GCM) with quadrupole-constrained Hartree-Fock-Bogoliubov (HFB) wavefunctions. Experimentally, 28Si presents shape coexistence between the oblate ground state and an excited prolate structure with bandhead at 6.7 MeV. Although the standard USDB interaction, which is very successful in describing the nuclear structure of nuclei in this mass region, reproduces well the oblate ground state, it fails at establishing a prolate band. Therefore, a modification of the USDB interaction must be introduced to reproduce the experimental spectrum. Guided by analytical Elliot’s SU(3) scheme, I show that this is achieved by slightly lowering the gap between the nearly degenerate 1d5/2-2s1/2 doublet and the 1d3/2 orbital. My calculations suggest that the oblate ground state is mostly 0p-0h configurations in the 1d5/2-2s1/2 orbitals, whereas the prolate band consists mainly of 4p-4h excitations into the 1d3/2 orbital. Additionally, I study whether 28Si can exhibit a superdeformed structure at higher energies. In order to achieve such deformations, excitations from the sd to the pf shell must be taken into account. I find that most of the deformation contribution comes from the 1f7/2-2p3/2 doublet and that the most favorable states are prolate 2p-2h and 4p-4h excitations into the pf shell. In contrast to previous studies, my numerical calculations suggest that this superdeformed structure would mix with normal-deformed configurations, and therefore 28Si would not present a superdeformed band.