Thermonuclear reaction rate of ${}^{30}\mathrm{Si}(p,\gamma ){}^{31}\mathrm{P}$

Silicon synthesis in high-temperature hydrogen burning environments presents one possible avenue for the study of abundance anomalies in globular clusters. This was suggested in a previous study, which found that the large uncertainties associated with the ${}^{30}\mathrm{Si}(p,\gamma ){}^{31}\mathrm{P}$ reaction rate preclude a firm understanding of the stellar conditions that give rise to the Mg-K anticorrelation observed in the globular cluster NGC 2419. In an effort to improve the reaction rate, we present new strength measurements of the $E_r^{\mathrm{lab}}=435$ keV and $E_r^{\mathrm{lab}}=501$ keV resonances in ${}^{30}\mathrm{Si}(p,\gamma ){}^{31}\mathrm{P}$. For the former, which was previously unobserved, we obtain a resonance strength of $\omega \gamma =(1.14\pm 0.25$) $\times {10}^{-4}$ eV. For the latter, we obtain a value of $\omega \gamma =(1.88\pm 0.14) \times {10}^{-1}$ eV, which has a smaller uncertainty compared to previously measured strengths. Based on these results, the thermonuclear reaction rate has been re-evaluated. The impact of the new measurements is to lower the reaction rate by a factor of $\approx 10$ at temperatures important to the study of NGC 2419. The rate uncertainty at these temperatures has also been reduced significantly.

Figure 1

Energy-level diagram of ${}^{31}\mathrm{P}$. Only levels relevant for the present work are displayed. Excitation energies and spin-parity values are adopted from multiple sources including the present work. See text for details.

Figure 2

Yield curves of the $E_r^{\mathrm{lab}}=622$ keV resonance in ${}^{30}\mathrm{Si}(p,\gamma ){}^{31}\mathrm{P}$. Both yields were measured at the start of the experiment in succession. The uncertainties shown derive from counting statistics only. The cyan area represents the $95\%$ credible region, as determined using a Bayesian method, to extract the maximum yield, target thickness, and area under the yield curve.

Figure 3

The LENA $\gamma \gamma$-coincidence spectrometer. A $135\%$ HPGe detector (yellow) is surrounded by a 16-segment NaI(Tl) annulus (green). The HPGe detector is located in close proximity to the target chamber for maximum efficiency. Not shown are the plastic scintillator paddles.

Figure 4

Measured singles (black) and coincidence (red) pulse-height spectra collected at the 435-keV resonance. Full-energy peaks are indicated for the primary transitions in ${}^{30}\mathrm{Si}(p,\gamma ){}^{31}\mathrm{P}$ and beam-induced contaminant reactions.

Figure 5

Contour plot of the ${}^{30}\mathrm{Si}(p,\gamma ){}^{31}\mathrm{P}$ reaction rate probability density as a function of temperature. The rate values are normalized to the recommended (median) rate. The shading indicates the coverage probability in percent. The thick and thin solid black lines indicate the high and low Monte Carlo rates for a coverage probability of $68\%$ and $95\%$, respectively.

Figure 6

The fractional contributions made by ${}^{30}\mathrm{Si}(p,\gamma ){}^{31}\mathrm{P}$ resonances and direct capture (labeled “DC”) toward the total reaction rate. The contribution ranges are shown as colored bands that correspond to their label above. The thickness of each band represents the uncertainty of the contribution. The dotted black line shows the contribution of resonances with energies larger than 648 keV.

Figure 7

Reaction rates from the present work (gray) and the evaluation of Iliadis et al. [51] (blue), normalized to the present recommended rates. The shaded areas correspond to $68\%$ coverage probabilities. The black solid line shows the ratio of the two recommended rates. Notice that the gray shaded area is the same as the area between the thick solid lines in Fig. 5.