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

TL;DR

This study uses shell-model calculations to explore shape coexistence in $^{28}$Si, revealing oblate, prolate, and superdeformed structures and how different interactions and configurations reproduce these shapes.

Contribution

It demonstrates that modifications to shell-model interactions and configurations can successfully reproduce multiple nuclear shapes in $^{28}$Si, including superdeformation.

Findings

The USDB interaction describes the oblate ground state well.

Prolate bands are reproduced by adjusting the $0d_{3/2}$ orbital energy.

Superdeformed structures appear at 18-20 MeV.

Abstract

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 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 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 $sdpf$ space. Our results indicate that superdeformed structures appear at about $18$-$20$~MeV.