Constraining the ${}^{30}\mathrm{P}(p,\gamma ){}^{31}\mathrm{S}$ Reaction Rate in ONe Novae via the Weak, Low-Energy, $\beta$-Delayed Proton Decay of ${}^{31}\mathrm{Cl}$

The ${}^{30}\mathrm{P}(p,\gamma ){}^{31}\mathrm{S}$ reaction plays an important role in understanding the nucleosynthesis of $A\ge 30$ nuclides in oxygen-neon novae. The Gaseous Detector with Germanium Tagging was used to measure ${}^{31}\mathrm{Cl}$ $\beta$-delayed proton decay through the key $J^{\pi }=3/2^{+}$, 260-keV resonance. The intensity $I_{\beta p}^{260}=8.3_{-0.9}^{+1.2}\times {10}^{-6}$ represents the weakest $\beta$-delayed, charged-particle emission ever measured below 400 keV, resulting in a proton branching ratio of ${\mathrm{\Gamma }}_p/\mathrm{\Gamma }=2.5_{-0.3}^{+0.4}\times {10}^{-4}$. By combining this measurement with shell-model calculations for ${\mathrm{\Gamma }}_{\gamma }$ and past work on other resonances, the total ${}^{30}\mathrm{P}(p,\gamma ){}^{31}\mathrm{S}$ rate has been determined with reduced uncertainty. The new rate has been used in hydrodynamic simulations to model the composition of nova ejecta, leading to a concrete prediction of ${}^{30}\mathrm{Si}$:${}^{28}\mathrm{Si}$ excesses in presolar nova grains and the calibration of nuclear thermometers.

Figure 1

${}^{31}\mathrm{Cl}$ $\beta$-delayed proton spectrum measured by only the central detector pad (black) and for event-level summing of the five inner detector pads [gray (pink online)] up to 1.5 MeV. The energy spectrum sums the ionization deposited in the P10 gas from both the decay protons and recoiling ${}^{30}\mathrm{P}$ nuclei. ${\beta }^{+}$ particles are responsible for the large background at low energies and can also sum with ionization produced by proton tracks, leading to a detector response that is skewed to the right; this effect is larger in the combined-pad spectrum due to the effective increase in detection pad area.

Figure 2

(a) Contributions of individual resonances to the ${}^{30}\mathrm{P}(p,\gamma ){}^{31}\mathrm{S}$ reaction rate and the total summed thermonuclear rate (solid black) plotted over peak nova temperatures. (b) The ratio between the experimental resonant reaction rate and the Hauser-Feshbach statistical rate [17]. The solid curve represents the recommended central rate, while the dashed curves indicate the upper and lower limits on the resonant rate calculation.