近日，北京应用物理与计算数学研究所的高翔及其研究团队取得一项新进展。经过不懈努力，他们利用光谱学和散射提出一种非里德伯共振态的扩展量子缺陷理论。相关研究成果已于2024年8月13日在国际知名学术期刊《物理评论A》上发表。

为兼顾非里德堡态计算的效率和数值精度，本文提出了一种非微扰计算方法。该方法首先应用本征通道R-矩阵方法处理排除非里德堡态的子系统，得到平滑变化的短程散射矩阵；随后，利用组态相互作用形式恢复非里德堡态；最后，通过简单的线性代数运算直接得到具有共振结构的散射矩阵。

由于该方法的各个组成部分都是能量的平滑函数，因此只需在稀疏的能量网格上进行耗时的从头计算，这使得该研究的方法计算效率极高，可视为传统MQDT的扩展。为证明本方法的有效性，研究人员计算了1分波中的共振+O⁺碰撞复合体。此外，研究人员还证明了非里德堡态对散射矩阵的数值精度有显著影响。

据悉，非里德堡共振态是一种具有开壳层电子构型的特殊共振态，其无法像里德堡态那样被划分为紧密耦合的离子靶和松散耦合的入射电子的准两体系统，是原子和分子系统中一类重要的共振过程。以往在多通道量子亏损理论（MQDT）框架下处理非里德堡共振态时，是将这些态作为MQDT参数平滑变化中的共振态引入，从而失去了MQDT方法在处理里德堡态时的主要优势。

附：英文原文

Title: Spectroscopy and scattering: An extended quantum defect theory for non-Rydberg resonant states

Author: Rui Sun, Rui Jin, Jia-Ming Li, Xiang Gao

Issue&Volume: 2024/08/13

Abstract: Non-Rydberg resonant states are a special type of resonant states with open-shell electronic configurations that cannot be partitioned into a quasi-two-body system of a tightly coupled ion target and a loosely coupled projectile electron as the case of Rydberg states, which is an important type of resonant processes in atomic and molecular systems. Previous treatments of non-Rydberg resonances in the context of multichannel quantum defect theory (MQDT) were to introduce these states as resonances in the smoothly varied MQDT parameters, and the main merit of the MQDT method for Rydberg states would be lost. To reconcile the efficiency and numerical accuracy for the calculation of non-Rydberg states, a nonperturbative calculation approach is proposed in this paper. In this approach, the smooth-varying short-range scattering matrices are obtained by applying the eigenchannel -matrix method to the subsystem excluding the non-Rydberg states. Subsequently, the non-Rydberg states are restored using the configuration-interaction formalism. The scattering matrices with resonant structures can then be obtained directly using simple linear algebra operations. Since the ingredients of the procedure are all smooth functions of energy, only a sparse energy grid is required for the time-consuming ab initio calculations. This makes our method highly computationally efficient and can be considered as an extension of the traditional MQDT. To demonstrate the efficacy of our method, the resonant +O⁺ collisional complex in the 1 partial wave is calculated. In addition, we demonstrate that the numerical accuracy of the scattering matrices is significantly affected by the non-Rydberg states.

DOI: 10.1103/PhysRevA.110.022806

Source: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.110.022806