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Manuscript Title: Coulomb functions in entire (eta,rho) - plane.
Authors: C. Bardin, Y. Dandeu, L. Gauthier, J. Guillermin, T. Lena, J.M. Pernet, H.H. Wolter, T. Tamura
Catalogue identifier: ABOQ_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 3(1972)73
Programming language: Fortran.
Computer: CDC 6600.
Operating system: UT-2.
RAM: 23K words
Word size: 60
Keywords: Schrodinger equation, Reactions, Scattering, Heavy ion, Wave function, Coulomb, Potential, Complex gamma function, Maclaurin expansion, Taylor expansion, Asymptotic expansion, Chebyshev expansion, Clenshaw expansion, Riccati Method, Confluent hypergeometric functions.
Classification: 4.5.

Nature of problem:
The subroutine COULOM calculates the regular and irregular Coulomb functions Fl(eta,rho) and Gl(eta,rho) and their derivatives for real positive energy in the whole (eta,rho)-plane (eta can take all values between and equal to -500 and 500, rho is greater than or equal to 0) with a uniformly high accuracy. This program will be useful, e.g., for the nuclear scattering and reaction calculations involving heavy projectiles, when rho is no longer very large compared with eta. It thus supplements existing programs that usually require rho much > (eta)**2.

Solution method:
The behaviour of the Coulomb functions in the (eta,rho)-plane varies widely. Of special importance is the transition time rho=2eta, where for l=0 the character changes from expotential to oscillatory. Different forms of expansions are chosen in different regions of the (eta,rho)-plane in a way similar but not identical to that of Froberg. These methods include Maclaurian expansion, Taylor expansion, asymptotic expansion, Chebychev expansion and Riccati method. A subroutine calculates the complex gamma function and its logarithmic derivative. The Coulomb functions for l>0 are calculated by using recursion relations employing a new technique recently proposed by Wills.

The parameters eta and rho have to be real. For complex eta and rho, due to complex energy, see Comp. Phys. Commun. 1(1969)25.