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.
Categories: nucl-th astro-ph.SR