Single and double photoemission and generalizations
  A unified diagrammatic treatment single and double electron photoemission currents is presented. The irreducible lesser density-density response function is the starting point of these derivations. Diagrams for higher order processes in which several electrons are observed in coincidence can likewise be obtained. For physically relevant situations in which the photoemission cross-section can be written as the Fermi Golden rule, the diagrams from the nonequilibrium Green's function approach can be put direct correspondence with that of the scattering theory. 
Yaroslav Pavlyukh
cond-mat.str-el