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[Background] Abundance anomalies in some globular clusters, such as theenhancement of potassium and the depletion of magnesium, can be explained interms of an earlier generation of stars polluting the presently observed ones.It was shown that the potential range of temperatures and densities of thepolluting sites depends on the strength of a few number of critical reactionrates. The reaction has been identified as one of these important reactions.[Purpose] The key ingredient for evaluating the thermonuclear reaction rate isthe strength of the resonances which, at low energy, are proportional to theirproton width. Therefore the goal of this work is to determine the proton widthsof unbound 31P states. [Method] States in 31P were studied at theMaier-Leibnitz-Laboratorium using the one-proton transfer reaction. Deuteronswere detected with the Q3D magnetic spectrometer. Angular distribution andspectroscopic factors were extracted for 27 states, and proton widths andresonance strengths were calculated for the unbound states. [Results] Severalunbound states have been observed for the first time in a one-proton transferreaction. Above 20 MK, the reaction rate is now entirely estimated from theobserved properties of states. The reaction rate uncertainty from allresonances other than the resonance has been reduced down to less than a factorof two above that temperature. The unknown spin and parity of the resonancedominates the uncertainty in the rate in the relevant temperature range.[Conclusion] The remaining source of uncertainty on the reaction rate comesfrom the unknown spin and parity of the resonance which can change the reactionrate by a factor of ten in the temperature range of interest.

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