where Ψ 1, … , 𝑁 and Ψ 2, … , 𝑁 are many-body wave functions of the initial N-electron and final N1 electron states, respectively. In the limit of a Hartree-Fock description of the Nelectron state and Koopmans approximation for the N1 electron state, Dyson orbitals correspond to the canonical Hartree-Fock (or Kohn-Sham) orbitals-hence, the latter are often used as an approximation to the Dyson orbitals computed from many-body wave functions. Plane-wave calculations. There are several approaches for the treatment of 𝜓 . Neglecting exit-channel interactions, the electron can be conveniently represented as a superposition of free spherical waves: