# Coulomb functions analytic in the energy

## Description

Abstract The Coulomb functions f(ϵ,l;ϱ) and g(ϵ,l;ϱ) are required for applications of quantum defect theory; ϵ is the Z-scaled energy, l the angular momentum quantum number and ϱ the Z-scaled radial coordinate. The functions f and g are analytic in ϵ. Power-series expansions are used to compute f and g and their derivatives with respect to ϱ. The computed value of the Wronskian gives an indication of the accuracy achieved. Title of program: COULAN Catalogue Id: AAJJ_v1_0 Nature of problem Quantum defect theory enables one to express values for various properties of atomic systems in terms of quantities which vary slowly as functions of the energy. In using the theory for ab-initio calculations, one requires the Coulomb functions f(epsilon, l; rho) and g(epsilon, l; rho) which are analytic in the energy variable epsilon. A program is provided for the computation of these functions. Versions of this program held in the CPC repository in Mendeley Data AAJJ_v1_0; COULAN; 10.1016/0010-4655(82)90047-9 This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2018)