Shape-excited states of²⁸Si

Abstract

The Hartree-Fock (HF) minima for the nucleus²⁸Si were obtained for the prolate, oblate and spherical shapes using the interaction obtained by Preedom and Wildenthal. The interaction gives rise to large energy separation between the prolate and the oblate shapes. The spherical solution is just 2 MeV above the lowest HF (oblate) minimum. The spectrum projected from the oblate HF state is in good agreement with the experimental spectrum. The transition probabilities for the different energy levels also agree reasonably well. The configuration mixing calculations performed on the basis of states projected from the three shapes indicate that there is no significant mixing of different projected states. The second 0 ⁺₂ state, thus obtained, corresponds to the third 0 ⁺₃ state in the experimental spectrum and stems dominantly from the spherical HF state. It is seen that the structure of the energy levels of²⁸Si, especially the second 0 ⁺₂ level is very sensitive to the two body interaction. The results are compared with those obtained using the renormalised interaction of Kuo.