Transition properties of low-lying states inSi28probed via inelastic proton andαscattering

Abstract

${0}^{+}, {1}^{\ensuremath{-}}, {2}^{+}$, and ${3}^{\ensuremath{-}}$ excitations of $^{28}\mathrm{Si}$ are investigated via proton and $\ensuremath{\alpha}$ inelastic scattering off $^{28}\mathrm{Si}$. The structure calculation of $^{28}\mathrm{Si}$ is performed with the energy variation after total angular momentum and parity projections in the framework of antisymmetrized molecular dynamics (AMD). As a result of the AMD calculation, the oblate ground and prolate bands, ${0}^{+}$ and ${3}^{\ensuremath{-}}$ excitations, and the ${1}^{\ensuremath{-}}$ and ${3}^{\ensuremath{-}}$ states of the ${K}^{\ensuremath{\pi}}={0}^{\ensuremath{-}}$ band are obtained. Using the matter and transition densities of $^{28}\mathrm{Si}$ obtained by AMD, microscopic coupled-channels calculations of proton and $\ensuremath{\alpha}$ scattering off $^{28}\mathrm{Si}$ are performed. The proton-$^{28}\mathrm{Si}$ potentials in the reaction calculation are microscopically derived by folding the Melbourne $g$-matrix $NN$ interaction with the AMD densities of $^{28}\mathrm{Si}$. The $\ensuremath{\alpha}\ensuremath{-}^{28}\mathrm{Si}$ potentials are obtained by folding the nucleon-$^{28}\mathrm{Si}$ potentials with an $\ensuremath{\alpha}$ density. The calculation reasonably reproduces the observed elastic and inelastic cross sections of proton and $\ensuremath{\alpha}$ scattering. Transition properties are discussed by combining the reaction analysis of proton and $\ensuremath{\alpha}$ scattering and structure features such as transition strengths and form factors. The isoscalar monopole and dipole transitions are focused.