Recently, a new $Δ$ method for the calculation of asymptotic normalization coefficients (ANC) from phase-shift data has been formulated, proved and used for bound states. This method differs from the conventional one by fitting only the nuclear part of the effective-range function which includes a partial phase shift. It should be applied to large-charge nuclei when the conventional effective-range expansion or the Padé-approximations using the effective-range function $K_l(k^2)$ fitting do not work. A typical example is the nucleus vertex $α+^{12}$C $\longleftrightarrow ^{16}$O. Here we apply the $Δ$ method, which totally excludes the effective-range function, to isolated resonance states. In fact, we return to the initial renormalized scattering amplitude with a denominator which defines the well-known pole condition. Concrete calculations are made for the resonances observed in the $^3$He-$^4$He, $α$-$α$, and $α$-$^{12}$C collisions. We use the experimental phase-shift and resonant energy data including their uncertainties and find the ANC variations for the states considered. The corresponding results are in a good agreement with those for the $S$-matrix pole method which uses the differing formalism. The simple formula for narrow resonances given in the literature is used to check the deduced results. The related ANC function clearly depends on the resonance energy ($E_0$) and width ($Γ$), which is used to find the ANC uncertainty ($Δ$ANC) through the energy ($ΔE_0$) and the width ($ΔΓ$) uncertainties.We also discuss the $Δ$ method differences between bound and resonance states pole conditions.
Relation between widths of proton resonances and neutron asymptotic normalization coefficients in mirror states of light nuclei in a microscopic cluster model
Deducing the asymptotic normalization constant of the 2+ subthreshold state in 16O from 12C + alpha elastic scattering
从最近的高精度测量的微分截面推导出的12 C + α弹性散射相移的R-矩阵分析进行。l=0的相移约束R矩阵半径a约5.85 fm，而l=2的相移导致既不对a也不对2+亚阈值状态的渐近归一化常数C（除了宽松的上限）的强约束。这与先前的12 C + α弹性散射的R矩阵分析相矛盾，并解释了在这些分析中获得的C值之间的不相容性。
Connection between asymptotic normalization coefficients and resonance widths of mirror states
渐近归一化系数（ANC）是在核反应、原子核结构和核天体物理中起重要作用的基本核常数。在本文中，ANC和镜态的共振宽度之间的联系建立。利用Pinkston-Satchler方程，由径向重叠函数和排除短程相互作用的二体薛定谔方程的正则解，用Wronskians表示，得到了镜核共振宽度和ANC的比值.该比率允许使用内部区域中的镜像核的微观重叠函数，其中它们是最准确的，以正确地预测镜像核的共振宽度和ANC的比率，其确定重叠函数的尾部的幅度。如果微观重叠函数不可用，则可以用相应的镜像两体势模型波函数来表示共振态和镜像束缚态的朗斯基函数。进一步简化朗斯基比，得到共振宽度和镜像ANC之比的方程，其表示为共振能和结合能处的两体库仑散射波函数之比[N. K.费尤克河C. Johnson和A. M. Mukhamedzhanov，Phys. Rev. Lett. { \bf 91}，232501（2003）。本文计算了不同核的共振宽度比和镜像ANC。如果反射镜ANC是已知的，则可以从该比率确定谐振宽度，反之亦然。与现有的实验比率进行比较。
Clarification of the relationship between bound and scattering states in quantum mechanics: Application to 12C + alpha
利用相位等效的超对称伙伴势，说明了量子散射理论中反问题的一般结果，即，从原理上讲，束缚态的性质不能从单个分波的相移中提取出来。特别是，最近的R-矩阵分析的12 C + α系统，提取渐近归一化常数的2+亚阈值状态，C12，从l=2的弹性散射相移和束缚态能量，被证明是不可靠的。相反，在核天体物理学中，这个重要的常数可以从简化势模型中l=0，2，4，6分波的同时分析中推导出来。一个新的超对称反转势和现有的模型给出C_（12）=144500+-8500 fm ~（-12）。
An essential singularity of the cotangent of the Coulomb-nuclear phase shift, and a finite limit of the nuclear part of the effective-range function derived at zero energy
Asymptotic normalization coefficients for $α+ {}^{12}{\rm C}$ synthesis and the $S$-factor for ${}^{12}{\rm C}(α, \,γ){}^{16}{\rm O}$ radiative capture
本文研究了亚阈值渐近归一化系数对$^{12}{\ m C}(α,γ)^{16}$O反应低能$S$因子的影响，分析了ANCs变化、共振贡献、不确定性及干涉效应，揭示了其在核天体物理中的关键作用。
Astrophysical $S$ factor for the ${}^{15}{\rm N}(p,γ){}^{16}{\rm O}$ reaction from $R$-matrix analysis and asymptotic normalization coefficient for ${}^{16}{\rm O} \to {}^{15}{\rm N} + p$. Is any fit acceptable?
$^{15}{\rm N}(p,γ)^{16}{\rm O}$反应提供了从CN循环到CNO双环和CNO三环的路径。测量的天体物理因素，这个反应是占主导地位的共振捕获通过两个强$J^π=1^{-}$共振在$E_{R}= 312$和962千电子伏和直接捕获到基态。最近，已经公布了$^{15}{\rm N}(p,γ)^{16}{\rm O}$反应的天体物理因子的新测量[P. J. LeBlanc { \it et al.}，{ \bf C 82}，055804（2010）]。分析已完成使用$R$ -矩阵的方法与无约束的变化的所有参数，包括渐近归一化系数（ANC）。已获得ANC $C^{2}= 539.2$ fm ${}^{-1}$的平方的最佳拟合，其超过先前测量值的因子$\approx 3$。在这里，我们提出了一个新的$R$ -矩阵分析的圣母院-月球数据与固定的实验不确定性平方内的ANC $C^{2}=200.34$ FM ${}^{-1}$。我们不是改变ANC，而是添加来自背景共振的贡献，该背景共振有效地考虑了来自更高水平的贡献。我们总共提出了8个配合，五个无约束和三个约束。在所有拟合中，ANC固定在先前确定的实验值$C^{2}=200.34$ fm ${}^{-1}$。对于具有边界条件$B_{c}=S_{c}(E_{2})$的无约束拟合，其中$E_{2}$是第二能级的能量，我们得到$…
