Background: Abundance anomalies in some globular clusters, such as the enhancement of potassium and the depletion of magnesium, can be explained in terms of an earlier generation of stars polluting the presently observed ones. It was shown that the potential range of temperatures and densities of the polluting sites depends on the strength of a few critical reaction rates. The ${}^{30}\mathrm{Si}(p,\gamma ){}^{31}\mathrm{P}$ reaction has been identified as one of these important reactions.

Purpose: The key ingredient for evaluating the thermonuclear ${}^{30}\mathrm{Si}(p,\gamma ){}^{31}\mathrm{P}$ reaction rate is the strength of the resonances which, at low energy, are proportional to their proton width. Therefore, the goal of this work is to determine the proton widths of unbound ${}^{31}\mathrm{P}$ states.

Method: States in ${}^{31}\mathrm{P}$ were studied at the Maier-Leibnitz-Laboratorium using the one-proton ${}^{30}\mathrm{Si}({}^3\mathrm{He},d){}^{31}\mathrm{P}$ transfer reaction. Deuterons were detected with the high resolution one quadrupole three dipoles (Q3D) magnetic spectrometer. Angular distribution and spectroscopic factors were extracted for 27 states, and proton widths and resonance strengths were calculated for the unbound states.

Results: Several ${}^{31}\mathrm{P}$ unbound states have been observed for the first time in a one-proton transfer reaction. Above 20 MK, the ${}^{30}\mathrm{Si}(p,\gamma ){}^{31}\mathrm{P}$ reaction rate is now entirely estimated from the observed properties of ${}^{31}\mathrm{P}$ states. The reaction rate uncertainty from all resonances other than the $E_r^{\text{c.m.}}=149$ keV resonance has been reduced down to less than a factor of 2 above that temperature. The unknown spin and parity of the $E_r^{\text{c.m.}}=149$ keV resonance dominates the uncertainty in the rate in the relevant temperature range.

Conclusion: The remaining source of uncertainty on the ${}^{30}\mathrm{Si}(p,\gamma ){}^{31}\mathrm{P}$ reaction rate comes from the unknown spin and parity of the $E_r^{\text{c.m.}}=149$ keV resonance which can change the reaction rate by a factor of 10 in the temperature range of interest.

• Received 16 July 2021
• Accepted 21 December 2021

DOI:https://doi.org/10.1103/PhysRevC.105.015805