Emission of correlated electron pairs from solid surfaces

Low-energy electron pairs, which are emitted from solid surfaces upon impact of a photon [(gamma,2e) process] or an electron [(e,2e) process] carry information on the exchange and screened Coulomb interaction between the two electrons inside the solid. We present a method for calculating such correlated two-electron states as antisymmetrized products of two one-electron states coupled by a correlation factor, which depends upon the one-electron quantum numbers and the relative spatial coordinate. The resulting pair correlation functions are illustrated for the cases of two plane-wave electrons interacting via a bare and a screened Coulomb potential. Low-energy electron diffraction-type one-electron states are then coupled in this manner and employed as final pair states in calculations of (e,2e) and (gamma,2e) reaction cross sections from the Cu(111) surface. For (e,2e), the angular distributions calculated without and with Coulomb interaction U exhibit, for antiparallel spins, a distinct correlation hole. For parallel spins, a large hole, which is already present without U, is enhanced. The (gamma,2e) distributions, which originate from the screened U inside the solid, have a large central region of enhanced intensity for antiparallel spins, out of which the exchange interaction carves a sizable hole. In all cases, the bare Coulomb repulsion on the way from the surface to the detectors reduces the intensity to zero for equal momenta of the two electrons.