α-planar states in28Si

Abstract

\ensuremath{\alpha}-planar states in ${}^{28}\mathrm{Si}$ are studied by employing the isomorphic shell model which uses no adjustable parameters. In the model, possible \ensuremath{\alpha} particles and their spatial distribution are derived, instead of being assumed as usual in \ensuremath{\alpha}-cluster models. Oblate triaxial structure for the ground state and a seven \ensuremath{\alpha}-particle planar structure for states with hexadecapole deformation have been found. Predictions of ground state and excited rotational bands and of other observables have been made and results are successfully compared with experimental data and those of other models where available. The novelty of the present study is focused on the fact that the axis of rotation changes within the ground state band and that the mentioned \ensuremath{\alpha}-planar structure originates four rotational bands two of which exhibit an almost rigid body rotation supporting a superdeformation for ${}^{28}\mathrm{Si}.$ The resonances of ${}^{12}{\mathrm{C}+}^{16}\mathrm{O}$ at 32.20 MeV, ${I}^{\ensuremath{\pi}}{=16}^{+},$ and at 46.2 MeV and 43.6 MeV, ${I}^{\ensuremath{\pi}}{=14}^{+},$ decaying to known planar states of light $4n$ nuclei, have been verified as members of three of the above four excited bands, thus supporting the proposed planar structure of ${}^{28}\mathrm{Si}.$