Diagrammatic approaches to the inelastic propagator

Two different diagrammatic construction schemes for obtaining the propagator for inelastic electronic scattering are presented. Both are discussed for the three cases that the target molecule of interest is closed-shell itself or has a closed-shell anion or cation. The 'direct approach' yields the inelastic propagator directly, but has the drawback that it requires the evaluation of a large number of diagrams already in low orders. The 'Dyson approach' uses Dyson-type equations for the inelastic propagator and employs a diagrammatic construction scheme for the generalized one-particle densities only. It therefore requires a considerably lower number of diagrams. Results are given up to first order for both methods and all three cases. Alternative approaches are briefly discussed and compared with our methods