Relativistic Coulomb bremsstrahlung in soft-photon approximation

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 regionmore » where A varies rapidly with energy.« less