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Manuscript Title: Two-center Coulomb functions.
Authors: M. Hiyama, H. Nakamura
Program title: TCOULOM
Catalogue identifier: ADFY_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 103(1997)209
Programming language: Fortran.
Computer: HP 735.
Operating system: UNIX.
Keywords: General purpose, Schrodinger equation in, Spheroidal coordinates, Two-center, Coulomb function, Numerical solution.
Classification: 4.5.

Nature of problem:
Subroutine TCOULOM is a FORTRAN77 subroutine to calculate the regular two-center Coulomb functions for the positive energy, epsilon. This program requires six constants. R: internuclear distance, Z1 and Z2: two positive charges, m and q: quantum numbers, epsilon: energy of an outgoing electron. Atomic units are employed.

Solution method:
There are three main subroutines in this program. The first one is to estimate the separation constants. The chain equation is solved there (see ref. [1]). The other two are to obtain wavefunctions of the angular part, Ximq(eta;kappa,R), and of the radial part, Pimq(xi;kappa,R). The spheroidal angular variable eta ranges between -1 and 1, and the radial variable xi from 1 to infinity. Ximq(eta;kappa,R) is obtained by solving the Schrodinger equation numerically, where we put eta=tanh q. The integral range of q is (-infinity,infinity), but in practice the range between -4.5 and 4.5 was found to be enough. The Numerov method [2] is used to solve the differential equation. The boundary conditions are provided by power series expansions at both ends. Pimq(xi;kappa,R) is obtained by solving the corresponding Schrodinger equation with use of both forward and backward Numerov procedure (see ref. [2]).

Restrictions:
This program may be used to evaluate the two-center Coulomb functions for the positive energy epsilon. The two positive charges are assumed to satisfy the relation Z2 >= Z1. The wavefunction for the case of Z2 = Z1 also can be calculated using this program. m and q are positive integers. They correspond to magnetic and azimuthal quantum numbers. This program produces only regular solutions both for the angular and radial parts.

References:
[1] L.I. Ponomarev and L.N. Somov, J. Comp. Phys. 20(1976)183.
[2] H. Takagi and H. Nakamura, Report of The Institute for Plasma Physics, Nagoya University, IIPJ-AM-16 (1980).