Shell-model study of ^28Si: coexistence of oblate, prolate and superdeformed shapes

We study the shape coexistence in the nucleus ^28Si with the nuclear shell model using numerical diagonalizations complemented with variational calculations based on the projected generator-coordinate method. The theoretical electric quadrupole moments and transitions as well as the collective wavefunctions indicate that the standard USDB interaction in the sd shell describes well the ground-state oblate rotational band, but misses the experimental prolate band. Guided by the quasi-SU(3) model, we show that the prolate band can be reproduced in the sd shell by reducing the energy of the 0d_3/2 orbital. Alternatively, in the extended sdpf configuration space the SDPF-NR interaction, which describes well other Si isotopes, also reproduces the oblate and prolate bands. Finally, we address the possibility of superdeformation in ^28Si within the sdpf space. Our results disfavour the appearance of superdeformed states with excitation energy below 20 MeV.