(p,t) and (p,He3) reactions onS33

Angular distributions of the ${}_{}{}^{33}{}_{}{}^{}\mathrm{S}$($p$,$t$)${}_{}{}^{31}{}_{}{}^{}\mathrm{S}$ and ${}_{}{}^{33}{}_{}{}^{}\mathrm{S}$($p$,${}_{}{}^3{}_{}{}^{}\mathrm{He}$)${}_{}{}^{31}{}_{}{}^{}\mathrm{P}$ reactions have been measured at 40 MeV bombarding energy. Unambiguous spin parity assignments of $\frac{3}{2^{+}}$ are made to levels in ${}_{}{}^{31}{}_{}{}^{}\mathrm{S}$ at 3.44, 4.53, and 6.27 MeV excitation energy on the basis of the observed $L=0\mathrm{}$ admixtures in their angular distributions. The lowest $T=\frac{3}{2}$ state in ${}_{}{}^{31}{}_{}{}^{}\mathrm{S}$ was observed and its excitation energy determined to 6.268±0.010 MeV. The experimental differential cross sections of transitions to low-lying mirror pairs of even parity final states in ${}_{}{}^{31}{}_{}{}^{}\mathrm{S}$ and ${}_{}{}^{31}{}_{}{}^{}\mathrm{P}$ are compared to the results of microscopic distorted-wave Born-approximation calculations based on shell-model calculations.