标题： 将基态性质${}^6$Li 相互连接以及与散射数据连接 显示英文标题

标题： Connecting ground-state properties of ${}^6$Li to each other and to scattering data

摘要： 我们研究了$^6$Li 的渐近归一化系数 (ANC) 与$\alpha$-氘核系统中其他低能可观测量之间的关系。我们的分析使用了一组在{\it 从头计算}无核心壳模型与连续体 (NCSMC) 框架内进行的计算，采用了多种核子间相互作用和基组大小，并得到了${}^6$Li 氘核分离能介于 1.3 到 1.8 MeV 之间 [Phys. Rev. Lett. 129, 042503 (2022)]。这些 NCSMC 计算表明，在这个范围内，ANC 的平方与分离能强烈相关。在这项工作中，我们使用经验性的$R$-矩阵、单通道势和微扰方法来研究这种相关性的起源。我们表明，这种相关性出现的原因是当分离能变化时，$\alpha$-氘核中心势的深度仅发生很小的相对变化。然后我们研究了在理想情况下，当有低能数据且没有实验误差时，是否可以准确地从$\alpha$-氘核相移中提取 ANC。 我们发现，只要外推受已知束缚态极点位置的约束，并且在拟合函数中至少包含三项，$R$-矩阵和库仑修正有效范围理论（CM-ERE）都能提取出接近但不完全等于真实值的ANC。 $R$-矩阵方法在参数数量增加时收敛速度比CM-ERE更快，并且在包含低能和高能相移数据时也更稳健。 最后，我们的研究还表明，通过比较两种理论中使用的不同截断来简单量化不确定性是不准确的，并建议需要进一步研究从相移数据中提取的ANC的准确性。 显示英文摘要

摘要： We examine the relationship between the Asymptotic Normalization Coefficient (ANC) of $^6$Li and other low-energy observables in the $\alpha$-deuteron system. Our analysis uses a set of calculations carried out within the {\it ab initio} No Core Shell Model with Continuum (NCSMC) using a variety of inter-nucleon interactions and basis sizes, and yielding ${}^6$Li deuteron separation energies between 1.3 and 1.8 MeV [Phys. Rev. Lett. 129, 042503 (2022)]. These NCSMC calculations show that the square of the ANC is strongly correlated with the separation energy over this range. In this work, we investigate the origin of this correlation using the phenomenological $R$-matrix, a single-channel potential and a perturbative approach. We show that this correlation occurs because the depth of the $\alpha$-deuteron central potential changes by only a small relative amount as the separation energy varies. We then investigate if the ANC can be accurately extracted from $\alpha$-deuteron phase shifts in an ideal case in which low-energy data are available and there are no experimental errors. We find that both $R$-matrix and Coulomb-modified effective-range theory (CM-ERE) yield extracted ANCs close to, although not exactly equal to, the true value, provided the extrapolation is constrained by the known position of the bound-state pole and at least three terms are included in the fit function. The $R$-matrix approach converges faster than the CM-ERE as the number of parameters increases and is also more robust against the inclusion of low-energy and high-energy phase shift data. Finally, our study also shows that a naive quantification of uncertainties by comparing different truncations used in both theories is not accurate, and suggests the accuracy of ANCs extracted from phase shift data needs further investigation.