Angular distributions of differential cross sections and vector and tensor analyzing powers have been measured for transitions in ${}_{}{}^{31}{}_{}{}^{}\mathrm{P}$(d${,}^3$He${)}^{30}$Si and ${}_{}{}^{31}{}_{}{}^{}\mathrm{P}$(d,t${)}^{30}$P reactions at $E_d$≊16 Mev. Exact, finite-range distorted-wave Born-approximation analyses have been performed using S- and D-state amplitudes for the three-nucleon systems. Calculations have also been carried out by incorporating realistic three-body wave functions. A j dependence in tensor analyzing powers observed for the first time in (d${,}^3$He) and (d,t) reactions, can be reproduced in distorted-wave Born approximation calculations only by including a D-state amplitude for three-nucleon systems. We find that the tensor analyzing powers for j=$l_1$+(1/2 transfers exhibit significantly more pronounced D-state effects than those for j=$l_1$-(1/2 transfers. The analyzing powers along with the differential cross sections have been used to extract spectroscopic factors for the low-lying levels in ${}_{}{}^{30}{}_{}{}^{}\mathrm{Si}$ and ${}_{}{}^{30}{}_{}{}^{}\mathrm{P}$, and the results have been compared with recent sd–shell-model predictions.

• Received 2 May 1988

DOI:https://doi.org/10.1103/PhysRevC.38.1537