Calculation of the electron–electron bremsstrahlung cross-section in the field of atomic electrons

An accurate expression for the free electron–electron bremsstrahlung (ee-brems) cross-section was derived by Haug in 1975, but unfortunately it must be combined with a rather prosaic correction to account for electron binding in atoms. We report on a numerical calculation of the ee-brems cross-section which include the effect of binding explicitly from the outset. Electron–electron bremsstrahlung occurs when a photon is emitted during the collision of two electrons, and an accurate treatment of ee-brems is well-advised in light elements, where it is significant compared to the nuclear bremsstrahlung process dominating in heavier elements. Our calculation allows us to verify and refine the ee-brems cross-section calculation recommended as part of ICRU Report 37. The results are auspicious in that they confirm the validity of the recommended approximations for electrons with high incident energies and over most of the emitted photon energy range. For incident energies on the order of 1 MeV or lower, however, we find a considerable discrepancy between the ee-brems radiative cross-section obtained with the ICRU calculation and with our more accurate approach. Accordingly, we correct existing cross-section data tables for the EGSnrc radiation transport simulation software.