No abstract

No abstract

No abstract

The differential cross sections for high-energy bremsstrahlung and pair production in a screened Coulomb field are calculated without the use of the Born approximation. It is shown that for pair production the correction to the Born approximation occurs only for momentum transfers q of order mc, for any amount of screening. For bremsstrahlung, however, the correction is only important for q's of order (mc 2 /E)mc, where E is the energy of the electron. As in the case of no screening, the correction to the differential cross section for bremsstrahlung is found to be given by a factor multiplying the Bethe-Heitler cross section. It is then shown that the bremsstrahlung cross section integrated over the angles of the final electron is additive, just as in the case of pair production: one part is the Bethe-Heitler cross section including screening; to this is then added the Coulomb correction which is independent of screening.The cross sections are evaluated by using wave functions which are accurate in the region in space which contributes significantly to the matrix element. This region is determined by the order of magnitude of q, and different wave functions must be used in the regions (I) corresponding to #'s of order mc and (II) corresponding to q's of order (mc 2 /E)mc. In (I) the wave functions are obtained by an expansion in partial waves and use of a WKB method on the radial wave equation. In (II) we use a WKB technique on the three-dimensional wave equation itself. Corrections due to the use of Sommerfeld-Maue wave functions, which are solutions to the second-order Dirac equation, are shown to be negligible. Finally, the method is used to obtain the cross section for small-angle elastic scattering.OLSEN, MAXIMON, AND WERGELAND an unscreened atom. These calculations are, however, only used to obtain the Born approximation result.Finally, the electron wave functions studied here may be of interest for other high-energy electron processes. GENERAL DISCUSSIONWe consider first the general approach used in obtaining wave functions which are accurate in the regions of space from which there is a significant contribution to the matrix elements for bremsstrahlung and pair production. This is followed by a discussion of the salient features of the wave functions and the related cross sections.The method which has been used for calculating matrix elements is briefly this. The Born approximation is assumed to be nearly correct, that is, the regions in space which contribute significantly to the more accurate matrix element are assumed to be determined by the Born approximation matrix element. For bremsstrahlung and pair production the important regions in the Born approximation are determined by the factor exp(^q-r), where q is the momentum transfer to the nucleus. The most important contributions come, therefore, from regions where q-r^l. Again we use a result from the Born approximation, that for high energies the cross section is only significant for q~l and q~l/e, and these regions are of equal importance. Further...

No abstract