Evaluation of negative energy Coulomb (Whittaker) functions

Abstract This paper describes a code for evaluating exponentially decaying negative energy Coulomb functions and their first derivatives with respect to the radial variable. The functions, which correspond to Whittaker functions of the second kind, are obtained to high accuracy for a wide range of parameters using recurrence techniques. Title of program: whittaker_w Catalogue Id: ADSZ_v1_0 Nature of problem The closed-channel components of the asymptotic radial wave function corresponding to electron or positron scattering by atomic or molecular ions may be expressed in terms of negative energy Coulomb functions. The scattering observables are obtained from S or T matrices which in turn are obtained by matching the radial and asymptotic wavefunctions at a finite radial point. Recent large scale scattering calculations have required accurate values of the Coulomb functions at smaller ρ values and la ... Versions of this program held in the CPC repository in Mendeley Data ADSZ_v1_0; whittaker_w; 10.1016/j.comphy.2003.12.004 This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2018)

摘要 本文介绍了一套用于计算指数衰减负能库仑函数（exponentially decaying negative energy Coulomb functions）及其对径向变量（radial variable）的一阶导数（first derivatives）的代码。该函数对应第二类惠特克函数（Whittaker functions of the second kind），通过递推技术（recurrence techniques）可在宽泛的参数范围内获得高精度的计算结果。
程序名称：whittaker_w
目录编号：ADSZ_v1_0
问题描述：原子或分子离子对电子或正电子的散射所对应的渐近径向波函数（asymptotic radial wave function）的闭通道分量（closed-channel components），可通过负能库仑函数进行表达。散射观测量（scattering observables）由S矩阵（S matrices）或T矩阵（T matrices）推导得到，而这些矩阵又通过在有限径向点（finite radial point）处匹配径向波函数（radial wavefunctions）与渐近波函数（asymptotic wavefunctions）获得。近期的大规模散射计算（large scale scattering calculations）需要在更小的ρ取值下获取精确的库仑函数值，且……
Mendeley数据中的CPC程序库（CPC Program Library）版本：ADSZ_v1_0；whittaker_w；10.1016/j.comphy.2003.12.004
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（1969-2018年）