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Experiments on the formation of magnesium complexes in $^4$He nanodropletswere interpreted as the observation of the formation of weakly bound magnesiumcomplexes. We present results for single Mg and Mg dimer solvation using thehypernetted chain / Euler-Lagrange method as well as path integral Monte Carlosimulations. We find that the phonon-mediated, indirect Mg-Mg interaction addsan oscillatory component to the direct Mg-Mg interaction. We undertake astep-by-step examination of the ingredients of the calculation of thephonon-induced interaction, comparing the results of semi-analytic HNC-ELcalculations for bulk and single impurity results with experiments as well asMonte Carlo data. We do not find evidence for a sufficiently strong secondaryminimum in the effective Mg-Mg interaction to support a metastable state.

Solvation of Mg in Helium-4: Are there Meta-stable Mg Dimers ?