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Manuscript Title: Coulomb functions with complex angular momenta.
Authors: T. Takemasa, T. Tamura, H.H. Wolter
Program title: CCOULM
Catalogue identifier: ABND_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 17(1979)351
Programming language: Fortran.
Computer: CDC 6600.
Operating system: UT-2.
RAM: 11K words
Word size: 60
Keywords: General purpose, Schrodinger, Scattering, Reactions, Regge, Complex angular momentum, Wave function, Coulomb, Complex coulomb, Potential, Asymptotic expansion, Phase shift, Logarithm of complex Gamma function.
Classification: 4.5.

Nature of problem:
The subroutine CCOULM calculates regular and irregular Coulomb functions and their derivatives associated with complex angular momenta. This program may thus be used, for example, in locating Regge poles that appear in atomic and nuclear scattering problems.

Solution method:
The calulation utilizes the asymptotic expansion method of Froberg. When ths asymptotic expansion does not give a satisfactory result at a desired rho, a larger value is chosen for rho and the differential equation is solved inward for the irregular solution. Then the method of Wills is used to obtain the regular solution. The complex Coulomb phase shift is obtained by using a subroutine which calculates the logarithm of the gamma function for complex argument.

Restrictions:
Subroutine CCOULM can be used for real values rho and eta and for complex (as well as real) angular momentum l that satisfy the condition eta**2 << rho and |l|**2 << rho. Even when this condition is not fulfilled, the program may be used with somewhat reduced accuracy.

Running time:
The evaluation of regular and irregular Coulomb wave functions and their derivatives for a given value of l takes about 0.3 s of the CDC 6600 computer.