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We consider the vector emissivity of the polarized radiation transfer in a$\Lambda$-type atomic transition, which we recently proposed in order toaccount for both CRD and PRD contributions to the scattered radiation. Thisexpression 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 termsdescribing, respectively, one-photon and two-photon processes in a$\Lambda$-type atom, %the fully and partially redistributed radiations, andwhere "f.s." means that the corresponding term must be evaluated assuming anappropriate "flat spectrum" average of the incident radiation across thespectral line. In this follow up study, we explicitly consider the expressionsof these various terms for the case of a polarized multi-term atom, in order toderive the algebraic forms of the branching ratios between the CRD and PRDcontributions to the emissivity. In the limit of a two-term atom withnon-coherent lower-term, our results are shown to be in full agreement withthose recently derived by Bommier (2017)

Explicit Form of the Radiative and Collisional Branching Ratios in Polarized Radiation Transport with Coherent Scattering