In the explosive astrophysical environment of a type I x-ray burst, the low $Q$ value of 293(50) keV for proton capture on ${}^{30}\mathrm{S}$ induces a $(p,\gamma )(\gamma ,p)$ equilibrium that may lead to a waiting point in the rapid proton capture ($\mathit{rp}$) process at ${}^{30}\mathrm{S}$. The excitation energies of the first and candidate second $T=3/2$ levels in ${}^{31}\mathrm{S}$ were recently determined to an uncertainty of 2 keV by measuring triton spectra and $t\text{−}p$ angular correlations from the ${}^{31}\mathrm{P}({}^3\mathrm{He},t){}^{31}\mathrm{S}{}^{*}(p){}^{30}\mathrm{P}$ reaction. By using this new information together with existing experimental information on the first $T=3/2$, $A=31$ isobaric multiplet and the isobaric multiplet mass equation, the ${}^{30}\mathrm{S}(p,\gamma ){}^{31}\mathrm{Cl}Q$ value is predicted to be 284(7) keV. Similarly, by using the second $T=3/2$ multiplet, the energy of the dominant resonance in the thermonuclear ${}^{30}\mathrm{S}(p,\gamma ){}^{31}\mathrm{Cl}$ reaction is tentatively predicted to be $E_{\mathrm{c}.\mathrm{m}.}=453(8)$ keV and this supports a ${}^{31}\mathrm{Ar}\hspace{0.5em}{\beta }^{+}$-delayed proton-decay observation of this resonance at $E_{\mathrm{c}.\mathrm{m}.}=461(15)$ keV. These substantial reductions in the uncertainties in the thermonuclear ${}^{30}\mathrm{S}(p,\gamma ){}^{31}\mathrm{Cl}$ reaction rate and $Q$ value constrain the region of temperature-density-composition parameter space where the ${}^{30}\mathrm{S}(p,\gamma )(\gamma ,p)$ equilibrium and the ${}^{30}\mathrm{S}$ waiting point may be active.

• Received 21 December 2008

DOI:https://doi.org/10.1103/PhysRevC.79.045808