Stimulated two-photon free-free transitions in a Coulomb potential: Formalism

Journal Article · Sun Jul 01 00:00:00 EDT 1990 · Physical Review, A (General Physics); (USA)

DOI:https://doi.org/10.1103/PhysRevA.42.236· OSTI ID:6416080

Gavrila, M ^[1]; Maquet, A; Veniard, V ^[2]

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1. FOM-Institute for Atomic and Molecular Physics, Kruislaan 407, 1098SJ Amsterdam (The Netherlands)
2. Laboratoire de Chimie Physique, Universite Pierre et Marie Curie, 11 rue Pierre et Marie Curie, F-75231 Paris CEDEX 05 (France)

We present a calculation of the cross sections for two-photon free-free transitions of an electron colliding with a Coulomb center of force. The calculation is based on second-order perturbation theory, in the nonrelativistic dipole approximation. The matrix elements for absorption and emission were integrated analytically in momentum space, following a method developed earlier by one of us. This makes use of the Schwinger integral representation for the Coulomb Green's function. The result was expressed in terms of integrals over hypergeometric functions of the Gauss type. Simple limiting forms of these complicated expressions were found in the first Born approximation, and at low and high photon energies. The results derived agree with those obtained by direct calculations done for these limits. Finally, concluding remarks on the analytic part of our work are made. The numerical computation of the two-photon free-free transition cross sections for absorption and emission in various geometries is planned to be presented at a later time.

• OSTI ID: 6416080
• Journal Information: Physical Review, A (General Physics); (USA), Vol. 42:1; ISSN 0556-2791
• Country of Publication: United States
• Language: English

Related Subjects

74 ATOMIC AND MOLECULAR PHYSICS
ELECTRON-ATOM COLLISIONS
BREMSSTRAHLUNG
COMPARATIVE EVALUATIONS
COULOMB FIELD
DIFFERENTIAL CROSS SECTIONS
ELECTROMAGNETIC FIELDS
GREEN FUNCTION
PERTURBATION THEORY
STIMULATED EMISSION
ATOM COLLISIONS
COLLISIONS
CROSS SECTIONS
ELECTRIC FIELDS
ELECTROMAGNETIC RADIATION
ELECTRON COLLISIONS
EMISSION
ENERGY-LEVEL TRANSITIONS
FUNCTIONS
RADIATIONS
640304* - Atomic
Molecular & Chemical Physics- Collision Phenomena