On Bremsstrahlung

Abstract

THE method previously used¹ to calculate the cross-section for pair production by a beam of γ-rays has been extended to deal with transitions of a Dirac electron between two states of positive energy in a Coulomb field. It is thus theoretically possible to obtain an exact evaluation of the differential cross-section for energy loss by radiation of an electron incident on an atomic field (neglecting screening, which is justifiable for the energy values used). Actually, owing to difficulties of computation, the calculation is only practicable for fairly slow electrons losing more than half their kinetic energy in the field of a heavy nucleus. This is the case in which the values calculated by th e use of Born's approximation² may be expected to be least reliable. The numerical work involved in the exact solution is too heavy to allow a full survey of the low energy region, so in order to check the Born values in this region the differential cross-section (per unit energy range of the final state) has been calculated in two particular cases, for lead (Z = 82) for an incident electron of total energy E₀ = 3mc², losing energy hv = l·5mc² and l·95mc².