Solvation of Mg in helium-4: Are there meta-stable Mg dimers?

Experiments with ⁴He nanodroplets doped with Mg atoms 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 (HNC-EL) 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.