Energy-Angle Distribution of Thin Target Bremsstrahlung

The differential bremsstrahlung cross section of Bethe and Heitler is integrated over scattered electron angles to obtain an expression for the distribution in energy and angle of the radiation from fast electrons in very thing targets. Screening is taken into account through the assumption of an atomic potential (Ze/r)exp(-r/a), and the calculation is restricted to high energies and to small to moderate angles. The result is the same as that of Sommerfeld for no screening, except that the argument of the logarithm now depends on angle as well as on energy. Integration of this expression over gamma-ray angle gives an analytic formula for the total intensity that is nowhere more than a few percent higher than the Bethe-Heither result calculated numerically on the basis of the Thomas-Fermi potential.