Critical sizes for the submersion of alkali clusters into liquid helium

Alkali atoms do not stably embed in liquid helium-4 because the interatomic attractive potential is unable to overcome the short-range Pauli repulsion of the s electrons and the surface tension cost of the surrounding bubble. Similarly, small alkali complexes reside on the surface of helium nanodroplets instead of inside. However, as the size of the metal cluster increases, its van der Waals attraction to the helium matrix grows faster than the repulsive energies and above a certain size it should become favorable for clusters to submerge in the liquid. Based on an evaluation of the relevant energy terms, we characterize the bubble dimensions and estimate the critical submersion sizes. The latter range from N similar to 20 for Li(N) and Na(N) to N > 100 for Rb(N) in helium-4 and from N similar to 5 for Li(N) and Na(N) to N similar to 20 for Cs(N) in helium-3. These results are discussed in the context of nanodroplet pick-up experiments with alkali atoms.