Level structure of ${}^{31}\mathrm{S}$ via ${}^{32}\mathrm{S}(p,d){}^{31}\mathrm{S}$

Background: Properties of proton-unbound ${}^{31}\mathrm{S}$ states determine the ${}^{30}\mathrm{P}(p,\gamma ){}^{31}\mathrm{S}$ 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 $3.285\le E_x\le 10.8$ MeV were momentum analyzed via an Enge split-pole spectrograph at six laboratory angles between ${10}^{\circ }$ and ${62}^{\circ }$. Differential cross sections of the ${}^{32}\mathrm{S}(p,d){}^{31}\mathrm{S}$ reaction were measured at $E_p=34.5$ 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 $E_x=6542$ keV, showing that is it not $J^{\pi }=3/2^{-}$, and therefore the contribution of this state to the ${}^{30}\mathrm{P}(p,\gamma )$ 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 ${}^{30}\mathrm{P}(p,\gamma ){}^{30}\mathrm{S}$ reaction rate over the temperatures characteristic of explosive hydrogen burning in novae.

Figure 1

Deuteron spectra measured from the ${}^{32}\mathrm{S}(p,d){}^{31}\mathrm{S}$ reaction at (a) ${62}^{\circ }$, (b) ${22}^{\circ }$, (c) ${20}^{\circ }$, and (d) ${10}^{\circ }$ obtained with the CdS target. ${}^{31}\mathrm{S}$ states are labeled with peak numbers corresponding to energies shown in Tables 1 and 2. Contaminant peaks are labeled by their parent nuclei. The shaded histograms are background spectra measured with a ${}^{\text{nat}}\mathrm{Cd}$ foil supported by a natural carbon backing, scaled to the background peaks of the ${}^{32}\mathrm{S}(p,d){}^{31}\mathrm{S}$ data. The background was not measured at ${62}^{\circ }$. For ${10}^{\circ }$ and ${20}^{\circ }$, an aluminum plate along the focal plane blocked the region corresponding to channels $\ge 2100$, where elastically scattered protons reached the focal plane.

Figure 2

Deuteron spectra from the ${}^{32}\mathrm{S}(p,d){}^{31}\mathrm{S}$ reaction measured at (a) ${45}^{\circ }$ and (b) $27.5^{\circ }$ obtained with the implanted target. ${}^{31}\mathrm{S}$ states are labeled with peak numbers corresponding to energies shown in Tables 1 and 2. Contaminant peaks are labeled by their parent nuclei. The shaded histograms are background spectra measured with an isotopically enriched ${}^{12}\mathrm{C}$ target, scaled to the background peaks of the ${}^{32}\mathrm{S}(p,d){}^{31}\mathrm{S}$ data. For $27.5^{\circ }$, an aluminum plate along the focal plane blocked the region corresponding to channels between $\approx 2300$–2500, where elastically scattered protons reached the focal plane. The ${22}^{\circ }$ spectrum obtained with the implanted target is not shown due to low statistics.

Figure 3

Deuteron angular distributions populating states of ${}^{31}\mathrm{S}$ compared with the theoretical DWBA curves. The filled circles with error bars (statistical in nature) are the measured relative differential cross sections in the center-of-mass system given in arbitrary units; and the solid, dashed, and dotted curves are the theoretical angular distributions obtained using dwuck5 [53]. If not shown, the error bar is smaller than the point size. The excitation energies (in keV) are given on the top middle of each plot.

Figure 4

Partial deuteron spectra from the ${}^{32}\mathrm{S}(p,d){}^{31}\mathrm{S}$ reaction, measured at (a) ${22}^{\circ }$, (b) ${20}^{\circ }$, and (c) ${10}^{\circ }$, which illustrate the individual Gaussian fits (in blue and orange), the total fits (in red), and the linear baselines (in green) for the states observed near $E_x=6.4$ MeV labeled with energies (in keV). Peak fitting was performed by using the minuit package [57] for python [58]. The channel numbers are different due to kinematics shift. The spectra are aligned by eye for clarity. ${\chi }_{\nu }^2$ of the fits varies between 1.36 at ${\theta }_{\mathrm{lab}}={10}^{\circ }$ to 1.58 at ${\theta }_{\mathrm{lab}}={22}^{\circ }$. All spectra are obtained using the CdS target. The 6377 keV state is respectively observed with a statistical significance of 1, 4.2, and 1.9 standard deviations at ${10}^{\circ }$, ${20}^{\circ }$, and ${22}^{\circ }$ above the background expectations, respectively.