Relativistic Coulomb bremsstrahlung in soft-photon approximation

Journal Article · Mon Apr 01 04:00:00 EST 1985 · Phys. Rev. A; (United States)

DOI:https://doi.org/10.1103/PhysRevA.31.2180· OSTI ID:5805362

Rosenberg, L

A low-frequency approximation for the bremsstrahlung transition amplitude is derived for a relativistic electron scattered by a central potential which is Coulombic at great distances. The Coulomb tail is shown here to have the effect of introducing correction terms, not present in previous relativistic treatments, which depend logarithmically on the photon frequency. The approximation procedure, in the form presented here, is based on the fact that at low frequencies the dominant contribution to the matrix element comes from the domain where r, the electron distance from the scattering center, is large. An asymptotic representation of the Dirac wave function is derived which includes a correction term of relative order 1/r compared to the leading term. This enables us to include a correction to the matrix element of relative order k, where k is the photon wave number. The essential feature of the low-frequency approximation, present in previous versions, is preserved here. That is, the result is expressed in terms of the physical amplitude, A, for scattering in the absence of any radiative interaction. Another potentially useful feature of the present version is that it involves angular derivatives of A, not energy derivatives, and should therefore remain valid in a region where A varies rapidly with energy.

• Research Organization: Department of Physics, New York University, New York, New York 10003
• OSTI ID: 5805362
• Journal Information: Phys. Rev. A; (United States), Journal Name: Phys. Rev. A; (United States) Vol. 31:4; ISSN PLRAA
• Country of Publication: United States
• Language: English

Related Subjects

645202* -- High Energy Physics-- Particle Interactions & Properties-Theoretical-- Electromagnetic Interactions & Properties
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
AMPLITUDES
ASYMPTOTIC SOLUTIONS
BREMSSTRAHLUNG
CENTRAL POTENTIAL
COULOMB FIELD
DIFFERENTIAL EQUATIONS
DIRAC EQUATION
DISTANCE
ELECTRIC FIELDS
ELECTROMAGNETIC RADIATION
ELECTRONS
ELEMENTARY PARTICLES
EMISSION
ENERGY RANGE
EQUATIONS
FERMIONS
INTERACTION RANGE
LEPTONS
PARTIAL DIFFERENTIAL EQUATIONS
PHOTON EMISSION
POTENTIALS
RADIATIONS
RELATIVISTIC RANGE
TRANSITION AMPLITUDES
WAVE EQUATIONS