Experimental study of the $^{30}$Si($^{3}$He,$d$)$^{31}$P reaction and thermonuclear reaction rate of $^{30}$Si($p$,$\gamma$)$^{31}$P

International audience[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 number of critical reaction rates. The reaction has been identified as one of these important reactions. [Purpose] The key ingredient for evaluating the thermonuclear 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 31P states. [Method] States in 31P were studied at the Maier-Leibnitz-Laboratorium using the one-proton transfer reaction. Deuterons were detected with the 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 unbound states have been observed for the first time in a one-proton transfer reaction. Above 20 MK, the reaction rate is now entirely estimated from the observed properties of states. The reaction rate uncertainty from all resonances other than the resonance has been reduced down to less than a factor of two above that temperature. The unknown spin and parity of the resonance dominates the uncertainty in the rate in the relevant temperature range. [Conclusion] The remaining source of uncertainty on the reaction rate comes from the unknown spin and parity of the resonance which can change the reaction rate by a factor of ten in the temperature range of interest