  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.

Nuclear Theory;Solar and Stellar Astrophysics