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Manuscript Title: Subroutines for the evaluation of cross sections of one-photon radiative processes occuring in fast-electron H-atom collisions.
Authors: A. Dubois, A. Maquet
Program title: FRFRTR
Catalogue identifier: ABTE_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 60(1990)271
Programming language: Fortran.
Operating system: DK1-6.0.2.
RAM: 10K words
Word size: 8
Peripherals: disc.
Keywords: Atomic physics, Photon, Laser-assisted electron, Atom, Collision, Free-free transitions, First born approximation, Coulomb green's function, Cross sections.
Classification: 2.5.

Nature of problem:
In the course of laser-assisted collisions of relatively fast electrons with hydrogen atom, the system can absorbe or emit a photon. Within a perturbative treatment of these free-free transitions, the total amplitude can be expressed, apart from an atomic form factor, in terms of second-order matrix elements containing the Coulomb Green's function. The present set of subroutines is designed to compute exactly these matrix elements which represent the main numerical difficulty and evaluate the cross sections for either absorption or stimulated emission.

Solution method:
Using a compact representation of the Coulomb Green's function, the transition amplitude is expressed in terms of only Gauss hypergeometric functions.

Within the framework of the lowest-order perturbative description of the couplings involved in the process (first Born approximation for the collision stage and one-photon exchange), the incoming electron energy must be much larger than 1 a.u., the laser intensity moderate and the frequency must be different from the atomic excitation frequencies.

Running time:
The evaluation of a cross section is less than 1 s.