In nebular astrophysics, there has been a long-standing dichotomy in plasma diagnostics between abundance determinations using the traditional method based on collisionally excited lines (CELs), on the one, hand and (optical) recombination lines/continuum, on the other. A number of mechanisms have been proposed to explain the dichotomy. Deep spectroscopy and recombination line analysis of emission line nebulae (planetary nebulae and HII regions) in the past decade have pointed to the existence of another previously unknown component of cold, H-deficient material as the culprit. Better constraints are needed on the physical conditions (electron temperature and density), chemical composition, mass, and spatial distribution of the postulated H-deficient inclusions in order to unravel their astrophysical origins. This requires knowledge of the relevant atomic parameters, most importantly the effective recombination coefficients of abundant heavy element ions such as CII, OII, NII, and NeII, appropriate for the physical conditions prevailing in those cold inclusions (e.g. Te<=1000K ).