Alpha clustering and alpha-capture reaction rate from ab initio symmetry-adapted description of ${}^{20}$Ne

Abstract

We introduce a new framework for studying clustering and for calculating alpha partial widths using ab initio wave functions. We demonstrate the formalism for ${}^{20}$Ne, by calculating the overlap between the ${}^{16}$O$+\alpha$ cluster configuration and states in ${}^{20}$Ne computed in the ab initio symmetry-adapted no-core shell model. We present spectroscopic amplitudes and spectroscopic factors, and compare those to no-core symplectic shell-model results in larger model spaces, to gain insight into the underlying physics that drives alpha-clustering. Specifically, we report on the alpha partial width of the lowest $1^{-}$ resonance in ${}^{20}$Ne, which is found to be in good agreement with experiment. We also present first no-core shell-model estimates for asymptotic normalization coefficients for the ground state, as well as for the first excited $4^{+}$ state in ${}^{20}$Ne that lies in a close proximity to the ${}^{16}$O$+\alpha$ threshold. This outcome highlights the importance of correlations for developing cluster structures and for describing alpha widths. The widths can then be used to calculate alpha-capture reaction rates for narrow resonances of interest to astrophysics. We explore the reaction rate for the alpha-capture reaction ${}^{16}$O$(\alpha ,\gamma {)}^{20}$Ne at astrophysically relevant temperatures and determine its impact on simulated X-ray burst abundances.

16 pages, 7 figures