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Manuscript Title: Coulomb functions for complex energies.
Authors: T. Tamura, F. Rybicki
Program title: COULOM
Catalogue identifier: ABOC_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 1(1969)25
Programming language: Fortran.
Computer: CDC 6600.
Operating system: CDC SCOPE.
RAM: 7K words
Word size: 60
Keywords: Nuclear physics, Schrodinger equation, Reactions, Potential, Complex gamma function, General purpose, Scattering, Wave function, Gamow function, Coulomb function.
Classification: 4.5.

Revision history:
Type Tit le Reference
correction 000A CORRECTION 18/03/72 See below

Nature of problem:
Subroutine COULOM is a Fortran IV subroutine to calculate the regular and irregular Coulomb functions and their derivatives for a complex energy E. This subroutine can be called with the following three quantities as input: Lmax, the maximum value of the orbital angular momentum; eta, the complex Coulomb parameter, and rho, the complex wave number times the radius. This subroutine may be used, for example, in calculating the wave function (Gamow function) that describes the decay of a nucleus by emitting a charged particle, tunneling through or going over the Coulomb barrier. In this case the imaginary parts of E, k, and (rho)**-1 are all negative. COULOM can, however, also be used if the imaginary parts of these quantities are positive or vanishing.

Solution method:
The method of calculation employed follows very closely that of Buck et al, who adapted the general method of Froberg to nuclear problems limited to the case of real energy. Froberg's formalism, however, works as well for complex E as it does for real E. Therefore, having a subroutine for the Coulomb functions for real E, a subroutine for complex E can be obtained by simply declaring most of the variables to be complex. The quantity sigma o, the complex Coulomb phase shift for the s-wave, needed in applying the method of Buck et al, is obtained in COULOM by using the formula exp(2isigma o) = Gamma(1+i eta)/Gamma(1-i eta) and by calling GAMMA, a subroutine which calculates the complex Gamma-function for complex arguments.

Restrictions:
This program may be used for a wide range of parameters that satisfy the condition |p|>>|eta**2|: Even if this condition is violated, the program may be used with somewhat reduced accuracy.

Running time:
The typical running time for Lmax~~10 is of the order of one-tenth of a second on the CDC 6600 computer.

CORRECTION SUMMARY
Manuscript Title: Coulomb functions for complex energies. (C.P.C. 1(1969)25).
Authors: T. Tamura, F. Rybicki
Program title: 000A CORRECTION 18/03/72
Catalogue identifier: ABOC_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 3(1972)276
Classification: 4.5.