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

Experiments on the formation of magnesium complexes in $^4$He nanodroplets were interpreted as the observation of the formation of weakly bound magnesium complexes. We present results for single Mg and Mg dimer solvation using the hypernetted chain / Euler-Lagrange method as well as path integral Monte Carlo simulations. We find that the phonon-mediated, indirect Mg-Mg interaction adds an oscillatory component to the direct Mg-Mg interaction. We undertake a step-by-step examination of the ingredients of the calculation of the phonon-induced interaction, comparing the results of semi-analytic HNC-EL calculations for bulk and single impurity results with experiments as well as Monte Carlo data. We do not find evidence for a sufficiently strong secondary minimum in the effective Mg-Mg interaction to support a metastable state.