Nuclear deformations ofMg24,Si28, andS32from fast neutron scattering

Abstract

Nuclear deformation of the $s\ensuremath{-}d$ shell nuclei $^{24}\mathrm{Mg}$, $^{28}\mathrm{Si}$, and $^{32}\mathrm{S}$ has been investigated by means of fast neutron scattering. Differential cross sections have been measured at the incident neutron energies of 9.76 and 14.83 MeV, over the angular range from 15\ifmmode^\circ\else\textdegree\fi{} to 160\ifmmode^\circ\else\textdegree\fi{}. Angular distributions have been obtained for the elastic scattering and the inelastic scattering to low lying collective states. The measurements have been compared to the predictions of collective models, and nuclear deformations have been determined for these nuclei. The coupled-channel and compound-nucleus formalisms were used in the calculations. The analysis shows that these nuclei exhibit quite different shapes, and confirms the oblate deformation of $^{28}\mathrm{Si}$ established in recent works. A detailed comparison of the deformations obtained in this study with those deduced from (p,p\ensuremath{'}), (d,d\ensuremath{'}), ($\ensuremath{\alpha}$,${\ensuremath{\alpha}}^{\ensuremath{'}}$), ($^{16}\mathrm{O}$, $^{16}\mathrm{O}\ensuremath{'}$), other (n,n\ensuremath{'}), and charge distribution measurements is presented and discussed. It is emphasized that for these $N=Z$ nuclei the quadrupole deformations and deformation lengths are in very good agreement when measured through neutron and proton scattering as well as electromagnetic excitations.