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arXiv 2006.08424nucl-th
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从$R$矩阵观点看光谱因子、重叠和同位旋对称性

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

Carl R. Brune

备注：
27 pages, 10 figures
发表信息：
Phys. Rev. C 102, 034328 (2020)
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摘要：

背景资料：在原子核结构和反应的唯象分析中，光谱因子、重叠和同位旋对称性常与单粒子波函数一起使用。许多不同的处方连接这些量的物理相关的渐近归一化常数或宽度在文献中，但它们的关系和有效性程度并不总是明确的。目的：本文使用定义明确的方法和起始假设推导出上述感兴趣的数量之间的关系。方法：$R$ -矩阵理论被用作主要工具，以相互操作的数量感兴趣的这项工作。特别注意所产生的影响超出核表面，那里的同位旋对称性强烈违反。结果：推导出感兴趣的量之间的关系。这些方法的例子应用于镜像核子+ ${}^{12}{\rm C}$，核子+ ${}^{16}{\rm O}$，和核子+ ${}^{26}{\rm Al}$水平。导出了一种新的多能级镜像对称性方法，并将其应用于${}^{18}{\rm O}$和${}^{18}{\rm Ne}$的前三个$2^+$态。结论：阐明了感兴趣的量之间的关系，并推荐了某些程序。发现由${}^{18}{\rm O}$中的镜像态推导出的${}^{18}{\rm Ne}$中第二个$2^+$态的渐近归一化常数明显大于以前的工作。这一发现具有增加新星中${}^{17}{\rm F}(p,γ){}^{18}{\rm Ne}$反应速率的作用。

英文摘要：

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+${}^{12}{\rm C}$, 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 asymptotic normalization constant 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 ${}^{17}{\rm F}(p,γ){}^{18}{\rm Ne}$ reaction rate in novae.

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