Absorption and emission line profile coefficients of multilevel atoms-III. Generalized atomic redistribution functions for three-photon processes

A previously published semiclassical formulation of the atomic line profile coefficients in terms of generalized redistribution functions is made more explicit by deriving atomic redistribution functions for three-photon processes. Quantum mechanical calculations are carried out for a general three-photon process corresponding to the atomic transition sequence i → j → k → f, for nondegenerate states i, j, k, f and within the framework of the impact approximation. For comparison, analogous calculations are also performed using the substate (Weisskopf-Woolley) picture. It is Found that the quantum mechanical and the substate forms of generalized redistribution functions agree in the limit of no collisions, whereas in the presence of collisions they agree only if level interface phenomena of the collisional line broadening are negligible. The physical assumption underlying the substate picture are discussed in detail.