Relativistic Positron-Electron Bremsstrahlung at Wide Angles: A Numerical Calculation

The bremsstrahlung spectrum for the process $e^{+}+e^{-}\to e^{+}+e^{-}+\gamma$ has been evaluated at photon-emission angles of roughly 30° to 120° from the incident particles in the c.m. system. The phase-space integrals of the exact, lowest-order differential cross section were evaluated numerically. A computer program was used to reduce the Dirac traces to invariants and to further simplify them until reasonably compact expressions were obtained. Numerical results for selected photon angles and energies are given for 15-BeV positrons incident upon electrons at rest in the laboratory and for 600- and 4000-MeV positrons in the c.m. system (colliding-beam experiments). It was found that certain relativistic approximations to the spectrum, which are valid for forward angles, are still fairly good at wide angles; an empirical modification to such an approximation is given which provides a useful interpolation formula for the wide-angle region.