  We consider the vector emissivity of the polarized radiation transfer in a
$\Lambda$-type atomic transition, which we recently proposed in order to
account for both CRD and PRD contributions to the scattered radiation. This
expression can concisely be written as
  $$\varepsilon=\left(\varepsilon^{(1)}
  -\varepsilon^{(2)}_{\rm f.s.} \right)
  +\varepsilon^{(2)}\;$$
  where $\varepsilon^{(1)}$ and $\varepsilon^{(2)}$ are the emissivity terms
describing, respectively, one-photon and two-photon processes in a
$\Lambda$-type atom, %the fully and partially redistributed radiations, and
where "f.s." means that the corresponding term must be evaluated assuming an
appropriate "flat spectrum" average of the incident radiation across the
spectral line. In this follow up study, we explicitly consider the expressions
of these various terms for the case of a polarized multi-term atom, in order to
derive the algebraic forms of the branching ratios between the CRD and PRD
contributions to the emissivity. In the limit of a two-term atom with
non-coherent lower-term, our results are shown to be in full agreement with
those recently derived by Bommier (2017)
