ULTRAVIOLET AND SOFT-X-RAY PHOTON-PHOTON ELASTIC-SCATTERING IN AN ELECTRON-GAS

We have considered the processes which lead to elastic scattering betw een two far ultraviolet or X-ray photons while they propagate inside a solid, modeled as a simple electron gas. The new ingredient, with res pect to the standard theory of photon-photon scattering in vacuum, is the presence of low-energy, nonrelativistic electron-hole excitations. Owing to the existence of two-photon vertices, the scattering process es in the metal are predominantly of second order, as opposed to fourt h order for the vacuum case. The main processes in second order are do minated by exchange of virtual plasmons between the two photons. For t wo photons of similar energy hBAROMEGA, this gives rise to a cross sec tion rising like OMEGA2 up to maximum of around 10(-32) cm2, and then decreasing like OMEGA-6. The maximal cross section is found for the ph oton wavevector k approximately k(F), the Fermi surface size, which ty pically means a photon energy hBAROMEGA in the keV range. Possible exp eriments aimed at checking the existence of these rare but seemingly m easurable elastic photon-photon scattering processes are discussed, us ing in particular intense synchrotron sources.