Abstract

Asymptotic normalization coefficients (ANCs) of the \(0_1^+\) , \(0_2^+\) , \(1_1^-\) , \(2_1^+\) , \(3_1^-\) ( \(l_{i th}^\pi \) ) bound states of \(^{16}\) O are deduced from the phase shift data of elastic \(\alpha \) - \(^{12}\) C scattering at low energies. S matrices of elastic \(\alpha \) - \(^{12}\) C scattering are constructed within cluster effective field theory (EFT), in which both bound and resonant states of \(^{16}\) O are considered. Parameters in the S matrices are fitted to the precise phase shift data below the p- \(^{15}\) N breakup energy for the partial waves of \(l=0,1,2,3,4,5,6\) , and the ANCs are calculated by using the wave function normalization factors of \(^{16}\) O propagators for \(l=0,1,2,3\) . We review the values of ANCs, which are compared with other results in the literature, and discuss uncertainties of the ANCs obtained from the elastic \(\alpha \) - \(^{12}\) C scattering data in cluster EFT.

中文翻译：

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$$^{16}$$ 束缚态的 ANC 从弹性 $$\alpha $$ - $$^{12}$$ C 散射数据推导

摘要

\ (0_1^+\)、\(0_2^+\)、\(1_1^-\)、\(2_1^+\)、\(3_1^-\) ( \( l_{i th}^\pi \) ) \(^{16}\) O的束缚态是根据弹性\(\alpha \) - \(^{12}\) C 散射的相移数据推导出来的低能量。弹性\(\alpha \) - \(^{12}\) C 散射的S矩阵是在簇有效场理论 (EFT) 内构建的，其中\(^{16}\) O 的束缚态和共振态均为经过考虑的。S矩阵中的参数适合\(l=0,1,2,3,4,5,6分波的p - \(^{15}\) N 破碎能以下的精确相移数据\) ，并使用\(^{16}\) O 传播器的波函数归一化因子计算\(l=0,1,2,3\)。我们回顾了 ANC 的值，将其与文献中的其他结果进行了比较，并讨论了从集群 EFT 中的弹性\(\alpha \) - \(^{12}\) C 散射数据获得的 ANC 的不确定性。