Astrophysical reaction rates from a symmetry-informed first-principles perspective

With a view toward a new unified formalism for studying bound and continuum states in nuclei, to understand stellar nucleosynthesis from a fully \emph{ab initio} perspective, we studied the nature of surface $\alpha$-clustering in $^{20}$Ne by considering the overlap of symplectic states with cluster-like states. We compute the spectroscopic amplitudes and factors, $\alpha$-decay width, and absolute resonance strength -- characterizing major contributions to the astrophysical reaction rate through a low-lying $1^-$ resonant state in $^{20}$Ne. As a next step, we consider a fully microscopic treatment for the $\mathrm{n}+^4$He system, based on the successful first-principles No-Core Shell Model/Resonating Group Method (NCSM/RGM) for light nuclei, but with the capability to reach intermediate-mass nuclei. The new model takes advantage of the symmetry-based concept central to the Symmetry-Adapted No-Core Shell Model (SA-NCSM) to reduce computational complexity in physically-informed and methodical way, with sights toward first-principles calculations of rates for important astrophysical reactions, such as the $^{23}\mathrm{Al}(\mathrm{p},\,\gamma)^{24}\mathrm{Si}$ reaction, believed to have a strong influence on X-ray burst light curves.