Recoil effects in high-energy photoemission beyond single-site approximation

Recoil effects of photoelectrons excited by high-energy X-rays are studied beyond the simplest approximation where elastic scatterings of photoelectrons are completely neglected (single-site approximation). At first we have shown that the simple free atom energy shift is accurately obtained within the harmonic and the single-site approximations. Beyond the single-site approximation, this simple formula does not work, but still simple classically acceptable formula can be used to explain the recoil energy shift. Illustrative numerical calculations show that the energy shifts caused by the photoelectron diffraction amounts to 5–8 meV for graphite-like carbon and about 100 meV for LiI₆${\text{LiI}}_6$ cluster at _?k=5${?}_k=5$–7 keV, and show oscillations as functions of the photoelectron energy. Furthermore we discuss the recoil effects in photoemission from extended levels by use of the tight-binding approach. Our approach naturally provides not only Debye–Waller factors but also the recoil factors. In addition to the phonon excitation, we also study the recoil effects associated with plasmon losses where intrinsic and extrinsic processes can interfere each other. Only the latter can contribute to the recoil energy shift.