Spectrum of Thin Target Bremsstrahlung Bounded by a Forward Circular Cone

Abstract

The Schiff expression for the cross section per nucleus, for thin-target bremsstrahlung into the angular and energy ranges dθ0 and dk, is integrated analytically over angle from zero to θ̄0. Results are shown for the case Z=78, E0 − mc2=40 Mev and x̄=0.5, 1, 2, 4, and 8, where E0 − mc2 is the kinetic energy of the incoming electron and x̄ is the reduced angle θ̄0E0/mc2. The fraction of the total cross section included in a cone of angle θ̄0 can be approximated to within 20% by x̄2/(1+x̄2). At x̄=1, or θ̄0=0.723°, the ratio of energy delivered by photons above (E0 − mc2)/2 to that below is 9% greater than for the limiting spectral shape at θ̄0=0, or that given by the Schiff expression at θ0=0, and 13% greater than for the spectrum integrated over all angles. For a target of finite thickness, multiple electron scattering should partially suppress the spectral dependence on x̄.