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

Abstract

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 between 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 among the quantities of interest are derived. Example applications of these methods to mirror levels in nucleon+${}^{12}\mathrm{C}$, nucleon+${}^{16}\mathrm{O}$, and nucleon+${}^{26}\mathrm{Al}$ are presented. A new approach to multi-level mirror symmetry is derived and applied to the first three $2^{+}$ states of ${}^{18}\mathrm{O}$ and ${}^{18}\mathrm{Ne}$. 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 ${}^{18}\mathrm{Ne}$ deduced from the mirror state in ${}^{18}\mathrm{O}$ is significantly larger than found in previous work. This finding has the effect of increasing the ${}^{17}\mathrm{F}(p,\gamma ){}^{18}\mathrm{Ne}$ reaction rate in novae.

27 pages, 10 figures

References in corpus (7)

• Shell Model in the Complex Energy Plane
• Asymptotic normalization coefficients from ab initio calculations
• New reaction rate for 16O(p,gamma)17F and its influence on the oxygen isotopic ratios in massive AGB stars
• Unitary correlation in nuclear reaction theory
• Precise Coulomb wave functions for a wide range of complex l, eta and z
• Ab initio calculations of nuclear widths via an integral relation
• To the Theory of Unstable States

Cited by in corpus (4)

• Deep underground laboratory measurement of ${}^{13}$C($\alpha$,$n$)${}^{16}$O in the Gamow windows of the $s$- and $i$-processes
• The study of the alpha formation probability in 10Be and 12Be within the microscopic cluster model
• Understanding the total width of the $3_1^{-}$ state in ${}^{12}\mathrm{C}$
• Green's Function Formalism for Impurity-Induced Resonances in Sub-barrier Proton-Nucleus Scattering