Level structure of S31 via S32(p,d)S31

Background: Properties of proton-unbound $^{31}\mathrm{S}$ states determine the $^{30}\mathrm{P}(p,\ensuremath{\gamma})^{31}\mathrm{S}$ reaction rate, which has a significant impact on explosive hydrogen burning in classical novae and type-I x-ray bursts. Despite several previous studies, uncertainties still remain with respect to the nuclear structure of $^{31}\mathrm{S}$ near the proton threshold.Purpose: The level structure of $^{31}\mathrm{S}$ has been presently investigated via a charged-particle spectroscopy experiment using the $^{32}\mathrm{S}(p,d)^{31}\mathrm{S}$ reaction.Method: Deuterons corresponding to $^{31}\mathrm{S}$ excited states with $3.285\ensuremath{\le}\phantom{\rule{4pt}{0ex}}{E}_{x}\phantom{\rule{4pt}{0ex}}\ensuremath{\le}10.8$ MeV were momentum analyzed via an Enge split-pole spectrograph at six laboratory angles between ${10}^{\ensuremath{\circ}}$ and ${62}^{\ensuremath{\circ}}$. Differential cross sections of the $^{32}\mathrm{S}(p,d)^{31}\mathrm{S}$ reaction were measured at ${E}_{p}\phantom{\rule{4pt}{0ex}}=34.5$ MeV. Distorted-wave Born approximation calculations were performed to constrain the spin-parity assignments of several of the observed levels.Results: We have detected 72 excited states of $^{31}\mathrm{S}$, out of which 17 are within the astrophysical region of interest corresponding to the temperature range of 0.1--1.5 GK. We have resolved the discrepancy in the spin and parity of an excited state with ${E}_{x}\phantom{\rule{4pt}{0ex}}=6542$ keV, showing that is it not ${J}^{\ensuremath{\pi}}\phantom{\rule{4pt}{0ex}}=3/{2}^{\ensuremath{-}}$, and therefore the contribution of this state to the $^{30}\mathrm{P}(p,\ensuremath{\gamma})$ reaction rate is likely much less significant than previously thought owing to the larger angular-momentum transfer required to populate this excited state. Moreover, our measurement results help consolidate the spin-parity assignments for the 6377 and 6636 keV states in $^{31}\mathrm{S}$.Conclusions: This work presents the most comprehensive spin-parity assignments to date from a single-neutron transfer reaction on $^{32}\mathrm{S}$ to $^{31}\mathrm{S}$ excited states in the region between 6 to 7 MeV excitation energy. This region is significant for the determination of the $^{30}\mathrm{P}(p,\ensuremath{\gamma})^{30}\mathrm{S}$ reaction rate over the temperatures characteristic of explosive hydrogen burning in novae.