Proton Hole States inAl29,P31, andP33

The low-lying states in ${}_{}{}^{29}{}_{}{}^{}\mathrm{Al}$, ${}_{}{}^{31}{}_{}{}^{}\mathrm{P}$, and ${}_{}{}^{33}{}_{}{}^{}\mathrm{P}$ have been studied via the reactions ${}_{}{}^{30}{}_{}{}^{}\mathrm{Si}(d, {}_{}{}^3{}_{}{}^{}\mathrm{He}){}_{}{}^{29}{}_{}{}^{}\mathrm{Al}$, ${}_{}{}^{26}{}_{}{}^{}\mathrm{Mg}(\alpha , p){}_{}{}^{29}{}_{}{}^{}\mathrm{Al}$, ${}_{}{}^{32}{}_{}{}^{}\mathrm{S}(d, {}_{}{}^3{}_{}{}^{}\mathrm{He}){}_{}{}^{31}{}_{}{}^{}\mathrm{P}$, ${}_{}{}^{34}{}_{}{}^{}\mathrm{S}(d, {}_{}{}^3{}_{}{}^{}\mathrm{He}){}_{}{}^{33}{}_{}{}^{}\mathrm{P}$, and ${}_{}{}^{30}{}_{}{}^{}\mathrm{Si}(\alpha , p){}_{}{}^{33}{}_{}{}^{}\mathrm{P}$. Spectroscopic factors have been extracted for the ($d$, ${}_{}{}^3{}_{}{}^{}\mathrm{He}$) reactions leading to two final states in ${}_{}{}^{29}{}_{}{}^{}\mathrm{Al}$, three in ${}_{}{}^{31}{}_{}{}^{}\mathrm{P}$, and two in ${}_{}{}^{33}{}_{}{}^{}\mathrm{P}$. In the ${}_{}{}^{30}{}_{}{}^{}\mathrm{Si}(d, {}_{}{}^3{}_{}{}^{}\mathrm{He}){}_{}{}^{29}{}_{}{}^{}\mathrm{Al}$ reaction, we observed $l=2\mathrm{}$ and $l=0\mathrm{}$ angular distributions from reactions leading to the ground state and first excited state, respectively. For the ${}_{}{}^{34}{}_{}{}^{}\mathrm{S}(d, {}_{}{}^3{}_{}{}^{}\mathrm{He}){}_{}{}^{33}{}_{}{}^{}\mathrm{P}$ reaction, we obtained an $l=0\mathrm{}$ distribution for the reaction to the ground state and an $l=2\mathrm{}$ distribution for the reaction to the second excited state.