Fast computer evaluation of radiative properties of hydrogenic systems

Abstract Three subroutines are described for the very fast calculation of bound-bound, bound-free, and free-free cross-sections for nonrelativistic hydrogenic systems of arbitrary nuclear charge and reduced mass. The first two are essentially exact, being based on recursion relations which are known to be stable. The third evaluates the thermally-averaged free-free Gaunt factor by means of a two-dimensional Chebyshev expansion calculated by numerical evaluation of the cross-sections expressed as hyper... Title of program: RADZ1 Catalogue Id: ABZS_v1_0 Nature of problem Although the cross sections for the absorption and emission of radiation by hydrogenic systems are known exactly in the nonrelativistic approximation, the analytic expressions are not easy to evaluate, especially for large values of the principal quantum number. However, for bound-bound and bound-free transitions, recursion techniques have proved to be accurate and stable for values of the principal quantum number as large as 500. For free-free transitions, recursion techniques are not applicabl ... Versions of this program held in the CPC repository in Mendeley Data ABZS_v1_0; RADZ1; 10.1016/0010-4655(91)90013-B This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2018)

**摘要**：本文描述了三个子程序，可用于极高速计算任意核电荷和约化质量的非相对论类氢系统的束缚-束缚、束缚-自由以及自由-自由截面。前两个子程序本质上精确，其基于已被证实稳定的递推关系。第三个子程序则通过对以超几何函数形式表达的截面进行数值计算得到二维切比雪夫展开式，以此计算热平均自由-自由冈特因子（Gaunt factor）。
**程序名称**：RADZ1
**目录编号**：ABZS_v1_0
**问题本质**：尽管非相对论近似下类氢系统的辐射吸收与发射截面已有精确解析解，但这些解析表达式难以直接计算，尤其当主量子数取值较大时。针对束缚-束缚与束缚-自由跃迁，递推方法已被证明在主量子数高达500的场景下仍具备准确性与稳定性。而对于自由-自由跃迁，递推方法并不适用……
**Mendeley数据集中CPC库保存的本程序版本**：ABZS_v1_0；RADZ1；10.1016/0010-4655(91)90013-B
本程序源自贝尔法斯特女王大学维护的CPC程序库（1969-2018）