Recoil Protons from Wide-Angle Bremsstrahlung

Abstract

Inelastic electron-proton scattering may be studied experimentally by momentum analyzing and detecting the final proton, in which case it becomes necessary to consider the contribution made by wide-angle bremsstrahlung. In this paper we calculate exactly the Bethe-Heitler contribution to the cross section for this process, differential in proton momentum and solid angle, and integrated over the phase space available to the unobserved final electron and photon. The result may be applied to muon-proton bremsstrahlung as well. If the electron rest mass is neglected where possible, the final formula takes a simple form as the sum of two terms. Of these, the dominant term containing a logarithm is proportional to the elastic scattering cross section, while the minor nonlogarithmic term can usually be neglected. The resulting formula is similar to that for the concomitant process in which the incoming electron radiates a photon in a physical radiator upstream and then scatters elastically from a proton, which in turn recoils into the detector. The factoring of the elastic scattering cross section occurs also when the final electron rather than the recoil proton is observed, a result which depends upon the so-called peaking approximation. In the present calculation the factoring of the leading term is exact for relativistic electrons.