Classical theory of Compton scattering: Assessing the validity of the Dirac-Lorentz equation

Journal Article · Mon Aug 01 04:00:00 EDT 2005 · Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

DOI:https://doi.org/10.1103/PhysRevE.72.026502· OSTI ID:20706339

Hartemann, F V; Gibson, D J; Kerman, A K ^[1]

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1. Lawrence Livermore National Laboratory, Livermore, California 94550 (United States)

The Dirac-Lorentz equation describes the dynamics of a classical point charge in an electromagnetic field, accounting for radiative effects in a manifestly covariant and gauge-invariant manner. The validity of this equation is assessed by direct comparison between the Dirac-Lorentz dynamics of an electron subjected to a plane wave in vacuum and the well-known recoil associated with Compton scattering. In the small recoil limit, the classical Dirac-Lorentz is shown to yield the correct momentum transfer. For larger values of the recoil, the quantum scale appears explicitly, and the classical Dirac-Lorentz equation does not properly model this situation, as shown by deriving an exact analytical solution for a monochromatic plane wave of wave number k{sub 0} to any order in k{sub 0}r{sub 0}, where r{sub 0} is the classical electron radius.

• OSTI ID: 20706339
• Journal Information: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, Journal Name: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics Journal Issue: 2 Vol. 72; ISSN PLEEE8; ISSN 1063-651X
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
COMPARATIVE EVALUATIONS
COMPTON EFFECT
DIFFERENTIAL EQUATIONS
ELECTROMAGNETIC FIELDS
ELECTRONS
GAUGE INVARIANCE
LORENTZ FORCE
MOMENTUM TRANSFER
MONOCHROMATIC RADIATION
QUANTUM ELECTRODYNAMICS
RECOILS