Measurements were made of the differential cross section for high-energy electron-proton scattering accompanied by either the emission of photons of various energies or low-energy pions. The dominant process studied was scattering of electrons accompanied by the emission of a single hard photon. The experiment was carried out by observing the spectrum of the inelastically scattered electron without observation of the recoil proton or emitted photon. The differential cross section for this process was computed theoretically by the numerical integration of a formula previously obtained by Berg and Lindner. The result of the integration yielded an approximate formula which expresses the cross section in terms of an "equivalent radiator." This formula was checked against both the more accurate computation and the experiment and found to be in good agreement. The theoretical expression for inelastic electron scattering is given in terms of the experimental measurements of elastic electron-proton scattering. The check of experiment against theory could be made insensitive to both the values of the elastic electron-proton cross sections assumed and to the absolute acceptance of the magnetic spectrometer used in the experiment by normalizing the observations to measurements of elastic electron-proton scattering.

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. I n 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. T h e 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. I n the present calculation the factoring of the leading term is exact for relativistic electrons.

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