(p,d) Reactions on Silicon Isotopes at 27.3 MeV

The neutron pick-up reactions ${}_{}{}^{29}{}_{}{}^{}\mathrm{Si}\mathrm{}(p,d)\mathrm{}{}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ and ${}_{}{}^{30}{}_{}{}^{}\mathrm{Si}\mathrm{}(p,d)\mathrm{}{}_{}{}^{29}{}_{}{}^{}\mathrm{Si}$ have been studied at a bombarding proton energy of 27.3 MeV. Several angular distributions were analyzed with the distortedwave Born approximation and the resulting spectroscopic factors and sum rule are given. The results indicate that the neutron configuration of the silicon isotopes contains $1d_{\frac{5}{2}}$, $2s_{\frac{1}{2}}$, and $1d_{\frac{3}{2}}$ components. A small $f$-wave neutron component has been found in ${}_{}{}^{30}{}_{}{}^{}\mathrm{Si}$. Strong $d_{\frac{5}{2}}$ transitions have been observed to the unresolved doublet ($J^{\pi }=3^{+},2^{+}$; $T=1\mathrm{}$) at 9.32 MeV in ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ and to the ($J^{\pi }={\frac{5}{2}}^{+}$; $T=\frac{3}{2}$) level at 8.32 MeV in ${}_{}{}^{29}{}_{}{}^{}\mathrm{Si}$. These states are the isobaric analogs to the states of ${}_{}{}^{28}{}_{}{}^{}\mathrm{Al}$ (0 and 0.031 MeV) and to the ground state of ${}_{}{}^{29}{}_{}{}^{}\mathrm{Al}$, respectively. The $J^{\pi }=4^{+}$ state at 4.61 MeV in ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ was excited in the ${}_{}{}^{29}{}_{}{}^{}\mathrm{Si}\mathrm{}(p,d)\mathrm{}{}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ reaction, indicating target excitation effects in single-nucleon-transfer reactions.