Correction to the formula for the radiative tail in elastic electron scattering

Abstract

The only major drawback in the use of the electron as a probc of nuclear structure m its tendency to radiate during scattering processes. The radiation effects require important corrections in the analysis of electron scattering experiments. Among the most important of these are the effects due to the interaction of the electron with the radiation field during scattering by the nucleus, causing it to emit real and vir tual photons, and thus modifying the scattering cross-section. Two types of such corrections must be considered: the radiative correction, which arises from the emission and re-absorption of virtual photons by the electron, and from the emission of soft, unobserved real photons, and the radiative tail, which consists of electrons which have emitted a hard photon during the scattering process, and whose energy has thus been degraded below the cut-off AE of the elastic peak. A theoretical expression for the radiative tail is obtained by integrating the crosssection for emission of a bremsstrahlung photon during the scattering process over the directions of the unobserved photon. All previous calculations (~) of the radiative tail have been limited by the use of the first Born approximation to describe the interaction of thc electron with the nucleus. A resilt which goes beyond the Born approxiination would be extremely useful, particularly in the analysis of electron scattering by heavy nuclei. However, the Bethe-Heitler cross-section (~) has been the only available useful expression for the bremsstrahlung cross-section, thus making it impossible to extend the calculation of the radiative tail beyond the first Born approximation. Recently, two independent calculations of the lowest-order correction to the BetheHeitler formula for bremsstrahlung by electrons scattered in a point Coulomb field have been made (3.4). In this paper we present an integration of this expression over the angles of the unobserved photon, using the peaking approximation due to SCHIF) (s).