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Connection between asymptotic normalization coefficients and resonance widths of mirror states

机译：镜面状态的渐近归一化系数与谐振宽度的连接

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Asymptotic normalization coefficients (ANCs) are fundamental nuclear constants that play an important role in nuclear reactions, nuclear structure, and nuclear astrophysics. In this paper a connection between ANCs and resonance widths of the mirror states is established. Using the Pinkston-Satchler equation the ratio for resonance widths and ANCs of mirror nuclei is obtained in terms of the Wronskians from the radial overlap functions and regular solutions of the two-body Schrodinger equation with the short-range interaction excluded. This ratio allows one to use microscopic overlap functions for mirror nuclei in the internal region, where they are the most accurate, to correctly predict the ratio of the resonance widths and ANCs for mirror nuclei, which determine the amplitudes of the tails of the overlap functions. If the microscopic overlap functions are not available one can express the Wronskians for the resonances and mirror bound states in terms of the corresponding mirror two-body potential-model wave functions. A further simplification of the Wronskian ratio leads to the equation for the ratio of the resonance widths and mirror ANCs, which is expressed in terms of the ratio of the twobody Coulomb scattering wave functions at the resonance energy and at the binding energy [N. K. Timofeyuk, R. C. Johnson, and A. M. Mukhamedzhanov, Phys. Rev. Lott. 1, 232501 (2003)]. Calculations of the ratios of resonance widths and mirror ANCs for different nuclei are presented. From this ratio one can determine the resonance width if the mirror ANC is known and vice versa. Comparisons with available experimental ratios are done.
机译：渐近标准化系数（ANC）是基本核常数在核反应，核结构和核天体物理学中发挥着重要作用。在本文中，建立了镜像状态的ANC和谐振宽度之间的连接。使用PINKSTON-Satchler方程，在从径向重叠功能和双体Schrodinger方程的径向重叠功能方面获得了镜子核的谐振宽度和ANC的比率，并排除了短距离相互作用。该比率允许一个用于在内部区域中使用微观重叠功能，在内部区域中，它们是最准确的，以正确地预测镜核的谐振宽度和ANC的比例，这决定了重叠函数的尾部的幅度。如果没有显微重叠功能，则可以在相应的镜像双体电位模型波函数方面表达谐振和镜界状态的谐振和镜界状态。 Fronskian比的进一步简化导致谐振宽度和镜子ANC的比率的等式，其就具有在谐振能量和结合能量处的Twobody Coulomb散射波函数的比率而表示[n。 K. Timofeyuk，R. C. Johnson和A. M. Mukhamedzhanov，Phy。 Rev. Lott。 1,232501（2003）]。介绍了不同核的共振宽度和镜子ANC比的计算。根据该比率，如果镜子ANC是已知的，则可以确定谐振宽度，反之亦然。采用可用实验比的比较。

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