Theory of recoil effects of elastically scattered electrons and of photoelectrons

Quasi-elastic scatterings of high-energy electrons are studied with quantum scattering theory including recoil effects by use of correlation functions. Two different types of recoil processes are investigated; one is free atom recoil and the other is phonon excited recoil processes within harmonic vibration approximation where Mermin's theorem works. The recoil effects of photoelectrons excited by high-energy X-rays are also studied, where the atomic displacement after the core-hole production also plays some important roles. For practical calculations the Debye approximation is used for phonon spectra, which gives rise to the simple free atom recoil energy shift. The broadenings of the spectra depend on the temperature in contrast to the energy shift, and is quite different from the free atom approximation in particular at low temperature. Numerical calculations are carried out for Be, C (graphite), Si and Ge powders. The energy shifts for solids composed of light elements are comparable with typical chemical shifts.