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

Background: Spectroscopic factors, overlaps, and isospin symmetry are often used in conjunction with single-particle wave functions for the phenomenological analysis of nuclear structure and reactions. Many differing prescriptions for connecting these quantities to physically relevant asymptotic normalization constants or widths are available in the literature, but their relationship and degree of validity are not always clear. Purpose: This paper derives relationships among the above quantities of interest using well-defined methodology and starting assumptions. Method: R-matrix theory is used as the primary tool to interoperate among the quantities of interest to this work. Particular attention is paid to effects arising from beyond the nuclear surface, where isospin symmetry is strongly violated. Results: Relationships between the quantities of interest are derived. Example applications of these methods to mirror levels in nucleon + C-12, + O-16, nucleon and nucleon Al-26 are presented. A new approach to multilevel mirror symmetry is derived and applied to the first three 2(-) states of O-18 and Ne-18. Conclusions: The relationship between the quantities of interest is clarified and certain procedures are recommended. It is found that the asymptotic normalization constant of the second 2(+) state in Ne-18 deduced from the mirror state in O-18 is significantly larger than found in previous work. This finding has the effect of increasing the F-17(p, gamma) Ne-18 reaction rate in novae.