Background] Spectroscopic factors, overlaps, and isospin symmetry are often used in conjunction with single-particle wavefunctions 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 between 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 between the quantities of interest are derived. Example applications of these methods to mirror levels in nucleon+$^{12}{\rm C}$, nucleon+$^{16}{\rm O}$, and nucleon+$^{26}{\rm Al}$ are presented. A new approach to multi-level mirror symmetry is derived and applied to the first three $2^{+}$ states of $^{18}{\rm O}$ and $^{18}{\rm Ne}$. [Conclusions] The relationship between the quantities of interest is clarified and certain procedures are recommended. It is found that the ANC of the second $2^{+}$ state in $^{18}{\rm Ne}$ deduced from the mirror state in $^{18}{\rm O}$ is significantly larger than found in previous work. This finding has the effect of increasing the $^{17}{\rm F}(p,\gamma)^{18}{\rm Ne}$ reaction rate in novae.

中文翻译：

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从𝑅矩阵的角度来看，光谱因素，重叠和同位旋对称

背景技术光谱因素，重叠和同位旋对称性经常与单粒子波函数结合用于核结构和反应的现象学分析。用于将这些数量与物理相关的渐近归一化常数或宽度相关联的许多不同的处方在文献中可用，但是它们之间的关系和有效性程度并不总是很清楚。[目的]本文使用明确定义的方法和起始假设来推导上述感兴趣数量之间的关系。[方法]$\mathrm{[R}$-矩阵理论被用作在此工作感兴趣的量之间进行互操作的主要工具。特别注意由于强烈违反同位旋对称性而从核表面以外产生的效应。[结果]得出感兴趣的量之间的关系。呈现了这些方法的示例应用，以反映核子+ $ ^ {12} {\ rm C} $，核子+ $ ^ {16} {\ rm O} $和核子+ $ ^ {26} {\ rm Al} $中的水平。推导了一种多级镜像对称的新方法，并将其应用于前三个$2^{+}$的状态$ ^ {18} {\ RMØ} $和$ ^ {18} {\ RM氖} $。[结论]阐明了感兴趣量之间的关系，并建议了某些程序。发现第二个ANC$2^{+}$在状态$ ^ {18} {\ RM氖} $从镜面状态推断$ ^ {18} {\ RMö} $是比以前的工作中发现显著大。该发现具有增加新星中$ ^ {17} {\ rm F}（p，\ gamma）^ {18} {\ rm Ne} $反应速率的效果。