A general program for computing matrix elements in atomic structure with nonorthogonal orbitals

Abstract To solve some problems concerning the atomic structure and transition probabilities, one needs to evaluate the matrix elements of various operators with respect to the configuration wave functions formed from the nonorthogonal one-particle orbitals. The program presented performs the angular integration necessary for expressing such matrix elements as weighted sums of radial integrals. Any amount of nonorthogonality between the orbitals may be presented leading to overlap integrals for the ma... Title of program: ZAP_NO Catalogue Id: ADDV_v1_0 Nature of problem In many atomic processes involving inner atomic shells, the relaxation of electron orbitals plays the important role. The relaxation can be most efficiently included into consideration by using the non-orthogonal orbitals for the initial and final state. This requires the evaluating of the matrix elements of various operators with respect to the non- orthogonal one-particle orbitals. Initially, these matrix elements can be expressed as weighted sums of relevant radial integrals, possibly multipl ... Versions of this program held in the CPC repository in Mendeley Data ADDV_v1_0; ZAP_NO; 10.1016/0010-4655(96)00079-3 This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2019)### 摘要 为解决与原子结构、跃迁概率相关的若干问题，需针对由非正交单粒子轨道（nonorthogonal one-particle orbitals）构建的组态波函数（configuration wave functions），计算各类算符的矩阵元（matrix elements）。本程序可完成必要的角积分（angular integration），将此类矩阵元表示为径向积分（radial integrals）的加权求和形式。程序支持任意程度的轨道非正交性，可导出对应矩阵的重叠积分（overlap integrals），原文此处截断为"ma..."。 程序名称：ZAP_NO 程序目录号：ADDV_v1_0 ### 问题本质 在诸多涉及原子内壳层的原子物理过程中，电子轨道的弛豫效应（relaxation）发挥着关键作用。若要在初态（initial state）与末态（final state）中采用非正交轨道以高效纳入弛豫效应的考量，则需针对非正交单粒子轨道计算各类算符的矩阵元。此类矩阵元最初可表示为相关径向积分的加权求和形式，原文此处截断为"multipl ..."。 ### 曼达莱数据（Mendeley Data）中的CPC程序库版本 存放在曼达莱数据中的CPC（Computer Physics Communications）程序库内的该程序版本信息为：ADDV_v1_0; ZAP_NO; 10.1016/0010-4655(96)00079-3 本程序源自贝尔法斯特女王大学（Queen's University Belfast）维护的CPC程序库（1969-2019年）。