Single proton transfer toP29,30states

Abstract

Differential cross sections were measured for the ($^{3}\mathrm{He},d$) reaction on $^{28}\mathrm{Si}$ and $^{29}\mathrm{Si}$ at ${E}_{^{3}\mathrm{He}}=25$ MeV by use of an Enge split-pole spectrometer. Up to 19 point angular distributions for transitions to 12 states in $^{29}\mathrm{P}$ below 6.4 MeV excitation energy and to 66 states in $^{30}\mathrm{P}$ below 8.7 MeV were analyzed in the distorted-wave Born approximation. The optical model parameters required for the distorted-wave Born approximation analysis were obtained from elastic $^{3}\mathrm{He}$ scattering data which were taken on $^{28}\mathrm{Si}$, $^{29}\mathrm{Si}$, and $^{30}\mathrm{Si}$. A number of $^{30}\mathrm{P}$ levels were found to have large components of simple two-particle structure, with one particle in the $2{s}_{\frac{1}{2}}$ shell and the other either in the $2{s}_{\frac{1}{2}}$, $1{d}_{\frac{3}{2}}$, $1{f}_{\frac{7}{2}}$, or $2{p}_{\frac{3}{2}}$ shells. Specifically, the states at 6092 and 7048 keV were assigned ${J}^{\ensuremath{\pi}}={3}^{\ensuremath{-}}$, $T=1$ and ${J}^{\ensuremath{\pi}}={4}^{\ensuremath{-}}$, $T=1$, respectively, because they were found to carry a significant fraction of the ($2{s}_{\frac{1}{2}}$) ($1{f}_{\frac{7}{2}}$) strength. However, the $T=0$ components of the $(2{s}_{\frac{1}{2}})_{}^{2}{}_{{1}^{+}}{}^{}$, ($2{s}_{\frac{1}{2}}$) ${(1{d}_{\frac{3}{2}})}_{{1}^{+}}$, and ${(1{d}_{\frac{5}{2}})}^{\ensuremath{-}1}(2{s}_{\frac{1}{2}})_{}^{3}{}_{{3}^{+}}{}^{}$ configurations were found to be distributed among a large number of states. Spin assignments were made based on shapes of the angular distributions and analog relations to $^{30}\mathrm{Si}$ states. An estmate of the extent to which the $1{d}_{\frac{5}{2}}$ proton shell is filled in $^{28}\mathrm{Si}$ and $^{29}\mathrm{Si}$ was extracted.