Investigation of $^{31}$P levels near the proton threshold by Nuclear Resonance Fluorescence and the impact on the $^{30}$Si(p,$\gamma$)$^{31}$P thermonuclear rate

We investigated the nuclear structure of $^{31}$P near the proton threshold using Nuclear Resonance Fluorescence (NRF) to refine the properties of key resonances in the $^{30}$Si(p,$\gamma$)$^{31}$P reaction, which is critical for nucleosynthesis in stellar environments. Excitation energies and spin-parities were determined for several states, including two unobserved resonances at $E_r$ $=$ $18.7$~keV and $E_r$ $=$ $50.5$~keV. The angular correlation analysis enabled the first unambiguous determination of the orbital angular momentum transfer for these states. These results provide a significant update to the $^{30}$Si(p,$\gamma$)$^{31}$P thermonuclear reaction rate, with direct implications for models of nucleosynthesis in globular clusters and other astrophysical sites. The revised rate is substantially lower than previous estimates at temperatures below $200$~MK, affecting predictions for silicon isotopic abundances in stellar environments. Our work demonstrates the power of NRF in constraining nuclear properties, and provides a framework for future studies of low-energy resonances relevant to astrophysical reaction rates.