  In previous papers of this series, we presented a formalism able to account
for both statistical equilibrium of a multilevel atom and coherent and
incoherent scatterings (partial redistribution). aims: This paper provides
theoretical expressions of the redistribution function for the two-term atom.
This redistribution function includes both coherent (R_II) and incoherent
(R_III) scattering contributions with their branching ratios. methods: The
expressions were derived by applying the formalism outlined above. The
statistical equilibrium equation for the atomic density matrix is first
formally solved in the case of the two-term atom with unpolarized and
infinitely sharp lower levels. Then the redistribution function is derived by
substituting this solution for the expression of the emissivity. results:
Expressions are provided for both magnetic and non-magnetic cases. Atomic fine
structure is taken into account. Expressions are also separately provided under
zero and non-zero hyperfine structure. conclusions: Redistribution functions
are widely used in radiative transfer codes. In our formulation, collisional
transitions between Zeeman sublevels within an atomic level (depolarizing
collisions effect) are taken into account when possible (i.e., in the
non-magnetic case). However, the need for a formal solution of the statistical
equilibrium as a preliminary step prevents us from taking into account
collisional transfers between the levels of the upper term. Accounting for
these collisional transfers could be done via a numerical solution of the
statistical equilibrium equation system.
