Compton-effect cross section for the electron gas: collective to single-particle transition

Calculations, within the SCF approximation, of the scattering cross section for the production of elementary excitations of the electron gas by high-energy photons are presented. The manner in which the cross section, dominated by plasmons at small momentum transfer, develops single-particle character with increasing momentum transfer is emphasized. It is shown that collective effects persist to wavevectors of the order of 6k F , where k F is the magnitude of the Fermi wavevector. This corresponds to a wavevector of about 9q c for a high electron-density gas (r s approximately 2) and 6q c for low electron-density gas (r s approximately 5), with q c the critical wavevector at which the onset of Landau damping occurs.