Absorption and emission line profile coefficients of multilevel atoms-IV. Velocity-averaged generalized redistribution functions for three-photon processes

The atomic generalized redistribution functions for three-photon processes, derived in the previous paper of this series, are formulated in terms of linear superpositions of newly introduced auxiliary functions q_I-q_VI, thus extending the traditional formalism of redistribution functions for two-photon processes. The corresponding velocity-averaged laboratory functions Q_I-Q_VI of these auxiliary functions are derived in both their angle-dependent and angle-averaged forms. Since the expressions found for Q_I-Q_VI are quite complicated, the so-called disentangled approximation is employed that uses the representative values of the generalized redistribution function at an orthogonal triad of photon directions rather than the angle-averaged function itself. This approximation yields relatively simple expressions which can be used in radiative transfer calculations.