Minimum sizes for the submersion of alkali clusters into liquid helium

TL;DR

This paper estimates the minimum alkali cluster sizes needed to submerge into liquid helium, based on energy considerations, highlighting size thresholds for different alkali metals in helium-4 and helium-3.

Contribution

It provides a theoretical evaluation of the critical sizes at which alkali clusters become energetically favorable to submerge in liquid helium, extending understanding of alkali-helium interactions.

Findings

Critical sizes range from N~20 for Li_N and Na_N in helium-4

Critical sizes range from N>100 for Rb_N in helium-4

Submersion becomes favorable beyond these sizes in helium-3 and helium-4

Abstract

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~20 for Li_N and Na_N to N>100 for Rb_N in helium-4 and from N~5 for Li_N and Na_N to N~20 for Cs_N in helium-3. These results are discussed in the context of nanodroplet pick-up experiments with alkali atoms