Structure of ${}^{30}\mathrm{S}$ with ${}^{32}\mathrm{S}$($p,t$)${}^{30}\mathrm{S}$ and the thermonuclear ${}^{29}\mathrm{P}$($p,\gamma$)${}^{30}\mathrm{S}$ reaction rate

The structure of proton unbound ${}^{30}\mathrm{S}$ states is important for determining the ${}^{29}\mathrm{P}$($p,\gamma$)${}^{30}\mathrm{S}$ 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, $J^{\pi }=$ $3^{+}$ 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 $J^{\pi }=3^{+}$. We have also discovered a new state at 4814(3) keV, which is a strong candidate for the other important resonance ($J^{\pi }=2^{+}$). The new ${}^{29}\mathrm{P}$($p,\gamma$)${}^{30}\mathrm{S}$ reaction rate is up to 4–20 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.

Figure 1

Triton spectra from the ${}^{32}\mathrm{S}$($p,t$)${}^{30}\mathrm{S}$ reaction. Peaks corresponding to ${}^{30}\mathrm{S}$ states are labeled with energies in keV. The solid histograms are background spectra measured with a Cd target on a carbon backing, normalized to the ${}^{32}\mathrm{S}$($p,t$)${}^{30}\mathrm{S}$ data. For ${10}^{°}$ and ${20}^{°}$, an aluminum plate along the focal plane blocked the channel region greater than $\approx$2000, where elastically scattered particles reached the focal plane. A few peaks from ${}^{13}\mathrm{C}$($p,t$)${}^{11}\mathrm{C}$ are also identified.

Figure 2

Level structures of ${}^{30}\mathrm{Si}$ [18] and ${}^{30}\mathrm{S}$ (present work) above the ${}^{29}\mathrm{P}+p$ threshold at 4399 keV and below 5.5 MeV. Dashed lines indicate proposed mirror assignments from the present work (see text).

Figure 3

(a) The new thermonuclear ${}^{29}\mathrm{P}$($p,\gamma$)${}^{30}\mathrm{S}$ reaction rate as a function of temperature. The 300-keV resonance controls the rate over the temperature range of 0.08 to 0.3 GK. The new 415-keV resonance, in turn, dominates the rate from 0.3 to 1.5 GK. (b) Variation in the present and previously determined reaction rates [6, 17] due solely to the uncertainties in the resonance energies.