Spectroscopic factors, overlaps, and isospin symmetry from an R -matrix point of view

$R$-matrix theory has long been used for phenomenological analyses of data from low-energy nuclear reactions, by connecting the interior nuclear structure to the exterior asymptotic continuum at a specified boundary channel radius. This paper reviews relationships of such quantities as interior spectroscopic amplitudes and single-particle wave functions with their physical counterparts such as asymptotic normalization coefficients and widths. The author provides examples in light nuclei including isospin and mirror symmetry applications to nucleosynthesis that suggest an enhanced ${}^{17}$F($p$,$\ensuremath{\gamma}$)${}^{18}$Ne reaction rate in novae.