Transition densities in ${}_{}{}^{30}{}_{}{}^{}\mathrm{Si}$ studied by electron scattering and coupled-channel calculations of 650 MeV proton scattering

Proton and neutron transition densities in ${}_{}{}^{30}{}_{}{}^{}\mathrm{Si}$ are examined by a combination of intermediate energy (e,e’) and (p,p’) reactions and mirror electromagnetic transition rates. This analysis is performed for the $2_1^{+}$ and $2_2^{+}$ states at 2.234 and 3.499 MeV in ${}_{}{}^{30}{}_{}{}^{}\mathrm{Si}$. Electron scattering data are presented for these states. Shell-model calculations for the proton and neutron transition matrix elements and proton transition densities are compared with the electromagnetic results. The proton transition densities are reasonably predicted for the $2_1^{+}$ state but are not adequately predicted for the $2_2^{+}$ state. A microscopic coupled-channel calculation of 650 MeV (p,p’) is used to test the shell-model isoscalar transition densities. Given the uncertainties present in the reaction calculation and interaction, the isoscalar density for the $2_1^{+}$ state is found to be adequate, but the density for the $2_2^{+}$ state is less accurate. The coupled-channel effect is shown to be important for the $2_2^{+}$ state. This dependence increases with energy but should be taken into account for an accurate description of (p,p’) reactions at all energies.