Quantum mechanical first Born binary encounter theory of electron impact ionization. II Electron Compton scattering

摘要

The first Born binary encounter theory of electron Compton scattering is developed. The theory includes the relationship between the usual xhyphen;ray Compton profile and its electron scattering counterpart including corrections for scattering from pairs of target electrons (a correction also necessary in the xhyphen;ray case at small scattering angles) and for exchange and interference scattering. In addition correction terms are derived for the difference between the complete first Born treatment and the binary encounter model. The corrections in the angular range of 10deg;ndash;60deg; at an incident electron energy of 25 keV are shown to be negligible. The target electron pair corrections at an incident electron energy of 25 keV are important only for small angle scattering for the lighter elements ( 7deg; for He) but may extend to larger angles for the heavier elements ( 30deg; for Ar). Exchange and interference between exchange and direct scattering become significant at the 1percnt; accuracy level at a scattering angle of 4deg; at the same incident energy. Between 4deg; and 45deg; interference between the exchange and direct amplitude dominates the correction term which can amount to 25percnt; of the direct scattering contribution at 35deg; although it largely vanishes at 45deg;. Beyond 45deg; the pure exchange terms rapidly dominate the scattering with increasing angle, and relativistic corrections become increasingly important. In this region the theory can break down and it is suggested that accurate experimental data could be helpful in arriving at a detailed description of the exchange process. A definition for an electron Compton profile including exchange and interference corrections from which the onehyphen;electron target momentum density can be extracted is suggested. The theory is also compared with recent experimental work for the case of He, and predictions for the scattered electron intensity as a function of energy loss and scattering angle are made for He at an incident electron energy of 25 keV.