Structure of S30 with S32(p,t)S30 and the thermonuclear P29(p,γ)S30 reaction rate

The structure of proton unbound $^{30}\mathrm{S}$ states is important for determining the $^{29}\mathrm{P}$($p,\ensuremath{\gamma}$)$^{30}\mathrm{S}$ reaction rate, which influences explosive hydrogen burning in classical novae and type I x-ray bursts. The reaction rate in this temperature regime had been previously predicted to be dominated by two low-lying, unobserved, ${J}^{\ensuremath{\pi}}=$ ${3}^{+}$ and ${2}^{+}$ resonances above the proton threshold in $^{30}\mathrm{S}$. To search for these levels, the structure of $^{30}\mathrm{S}$ was studied using the $^{32}\mathrm{S}$($p,t$)$^{30}\mathrm{S}$ transfer reaction with a magnetic spectrograph. We have confirmed a previous detection of a state near 4700 keV, which had tentatively been assigned ${J}^{\ensuremath{\pi}}={3}^{+}$. We have also discovered a new state at 4814(3) keV, which is a strong candidate for the other important resonance (${J}^{\ensuremath{\pi}}={2}^{+}$). The new $^{29}\mathrm{P}$($p,\ensuremath{\gamma}$)$^{30}\mathrm{S}$ reaction rate is up to 4\char21{}20 times larger than previously determined rates over the relevant temperature range. The uncertainty in the reaction rate due to uncertainties in the resonance energies has been significantly reduced.