Shell-model Study of 28 Si: Coexistence of Oblate, Prolate, and Superdeformed Shapes

We study the shape coexistence in the nucleus 28 Si 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 wave functions 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 0d3/2 orbital. Alternatively, in the extended sd pf configuration space a modification of the SDPF-NR interaction that accommodates cross-shell excitations also reproduces the oblate and prolate bands. Finally, we address the possibility of superdeformation in 28 Si within the sd pf space. Our results indicate that superdeformed structures appear at about 18-20 MeV.