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

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...

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Bibliographic Details
Published in:Physical review. A, Atomic, molecular, and optical physics Atomic, molecular, and optical physics, 1990-07, Vol.42 (1), p.236-247
Main Authors: GARVRILA, M, MAQUET, A, VENIARD, V
Format: Article
Language:English
Subjects:
640304 - Atomic, Molecular & Chemical Physics- Collision Phenomena
ATOM COLLISIONS
Atomic and molecular collision processes and interactions
ATOMIC AND MOLECULAR PHYSICS
BREMSSTRAHLUNG
COLLISIONS
COMPARATIVE EVALUATIONS
COULOMB FIELD
CROSS SECTIONS
DIFFERENTIAL CROSS SECTIONS
ELECTRIC FIELDS
ELECTROMAGNETIC FIELDS
ELECTROMAGNETIC RADIATION
ELECTRON COLLISIONS
Electron scattering
ELECTRON-ATOM COLLISIONS
EMISSION
ENERGY-LEVEL TRANSITIONS
Exact sciences and technology
FUNCTIONS
GREEN FUNCTION
PERTURBATION THEORY
Physics
RADIATIONS
STIMULATED EMISSION
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Summary: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.
ISSN:0556-2791
1050-2947
1094-1622
DOI:10.1103/PhysRevA.42.236