Single proton transfer toP29,30states

Differential cross sections were measured for the (${}_{}{}^3{}_{}{}^{}\mathrm{He},d$) reaction on ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ and ${}_{}{}^{29}{}_{}{}^{}\mathrm{Si}$ at $E_{{}_{}{}^3{}_{}{}^{}\mathrm{He}}=25\mathrm{}$ 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 $2s_{\frac{1}{2}}$ shell and the other either in the $2s_{\frac{1}{2}}$, $1d_{\frac{3}{2}}$, $1f_{\frac{7}{2}}$, or $2p_{\frac{3}{2}}$ shells. Specifically, the states at 6092 and 7048 keV were assigned $J^{\pi }=3^{-}$, $T=1\mathrm{}$ and $J^{\pi }=4^{-}$, $T=1\mathrm{}$, respectively, because they were found to carry a significant fraction of the ($2s_{\frac{1}{2}}$) ($1f_{\frac{7}{2}}$) strength. However, the $T=0\mathrm{}$ components of the