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Manuscript Title: Coulomb functions analytic in the energy.
Authors: M.J. Seaton
Program title: COULAN
Catalogue identifier: AAJJ_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 25(1982)87
Programming language: Fortran.
Computer: IBM 360/195.
Operating system: HASP-MVT.
RAM: 4K words
Word size: 64
Keywords: General purpose, Coulomb function, Quantum defect theory.
Classification: 4.5.

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.

Solution method:
Power-series expansions are used.

The computed value of the Wronskian gives an indication of the accuracy achieved. For the test run the fractional error in the Wronskian is not larger than 3.3E-09.

Running time:
About 5 ms to calculate two linearly independent Coulomb functions, and their derivatives, for one energy, one angular momentum, one radial distance.