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Manuscript Title: Radial electric multipole matrix elements for inelastic collisions in atomic and nuclear physics.
Authors: H.F. Arnoldus
Program title: CLMINT
Catalogue identifier: ACCM_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 32(1984)421
Programming language: Fortran.
Computer: BURROUGHS 7700.
Operating system: MCP (BURROUGHS), NOS/BE (CDC).
Word size: 52
Keywords: Atomic physics, Coulomb, Wave function, Heavy ions, Scattering, Matrix elements, Inelastic collisions, Wkb method.
Classification: 2.7.

Nature of problem:
Solution of the radial Schrodinger equation for inelastic collisions between charged particles requires matrix elements of electric multipole operators in the region of large r values. These matrix elements are in general integrals over a finite interval (R1, R2) of a product of Coulomb wave functions and a factor r(-lambda-1). Especially in the case of heavy ion collisions at high energy, these are very cumbersome integrals because the integrand is a rapidly oscillating function with a wavelength much smaller than the integration interval. When we choose R2 = infinity the convergence of the integral is very slow.

Solution method:
If we split up the integrand into a rapidly and a slowly varying function of the integration variable r, it is possible to construct an asymptotic series for the integral with the fast oscillating integrand. The remianing integral is easily obtained by Gaussian quadrature. Because we are integrating over large r values (compared to the classical turning points), it is possible to use the familiar WKB- approximation of Coulomb wave functions in the step-by-step integration. The subroutine has been set up to achieve a relative accuracy of 10**-7.

The subroutine has only been tested for significant 1, eta and k values i.e.0<=1<2000, 0>eta>1000, 0<k<50. The interval [R1,R2] can be any part of [0, infinity). When R1 does not exceed the lowest turning point especially R1=0), only the integrals with the regular Coulomb wave functions F1(eta,p) are reliable. Furthermore the case lambda=0 is not included.

Running time:
The running time depends strongly on the parameters and the lower limit R1. When R1 lies in the asymptotic region, as in practical applications, the running time will in general be a fraction of a second but for smaller R1 values it increases rather rapidly.