The 18.72-MeV differential cross sections for the ${\mathrm{P}}^{31}(\alpha ,d){\mathrm{S}}^{33}$ reactions leading to the ground and 0.841-MeV states of ${\mathrm{S}}^{33}$ have been measured from 15° to 170° at 5° intervals. The deuteron spectra were determined using a spectrometer configuration which incorporated an $E\times \Delta E$ mass identification system and an ($E,\Delta E$) counter telescope consisting of two silicon surface-barrier detectors. The target was prepared by the thermal vacuum evaporation of red phosphorus (650±12 μg/${\mathrm{cm}}^2$) onto a thin Formvar film (∼20 μg/${\mathrm{cm}}^2$). In contrast to the well-defined oscillatory shape of the angular distribution associated with the transition to the 0.841-MeV state, that corresponding to the transition to the ground state has only washed-out undulations. The integrated cross sections for the ground and 0.841-MeV state reactions are 724±16 μb (16.9°-171.3°) and 425±10 μb (17.0°-171.3°), respectively. An analysis of the data in the distorted-wave Born approximation has been made in terms of a zero-range, knock-out model in which the initial (final) nuclear state is represented as a two-body system with a deuteron (alpha particle) bound to a ${\mathrm{Si}}^{29}$ core. Good agreement between the experimental and theoretical angular distributions was achieved. The analyses require a $2s_{\frac{1}{2}}$ state for the ($d,{\mathrm{Si}}^{29}$) system representing the ground state of ${\mathrm{P}}^{31}$, and $1d_{\frac{3}{2}}$ and $2s_{\frac{1}{2}}$ states for the ($\alpha ,{\mathrm{Si}}^{29}$) system representing the ground and 0.841-MeV states of ${\mathrm{S}}^{33}$, respectively. An interpretation of the experimental results on the basis of the dominant shell-model configurations for the states of ${\mathrm{P}}^{31}$ and ${\mathrm{S}}^{33}$ yields the conclusion that there is no enhancement of the transition in which the members of the transferred nucleon pair enter equivalent orbitals relative to that in which the nucleons enter nonequivalent orbitals.

• Received 31 August 1966

DOI:https://doi.org/10.1103/PhysRev.153.1221