In the present work we take a closer look at the theoretical model of double-electron photoemission (DPE) we have introduced in [1,2]. A local wave-vector-dependent approximation of the Coulomb interaction between the photoelectrons gives a connection of DPE to the one-step model of single photoemission (SPE). Calculations of DPE photocurrent for Cu(001) and Cu(111) surfaces are provided to illustrate the interplay between scattering and correlation, as well as the manifestation of the single-particle properties in angular and energy sharing distributions.