Si28Nucleus in the Projected Hartree-Fock Model

Abstract

The structure of the ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ nucleus is studied using a variational procedure. The method of angular-momentum projection from a deformed intrinsic state is applied, and each $J^{\pi }$ state is projected from a determinant which is variationally "best" for that state. This more general variational procedure includes important vibrational correlations, which in ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ have hexadecapole character. The level spacings in the energy spectrum improve considerably compared to those in the Hartree-Fock method followed by angular momentum projection, and this leads to a much better agreement with the experimental spectrum. The $E2\mathrm{}$ transition probabilities, except for the $6^{+}$→$4^{+}$ transition, are also in good agreement with the experiments.