Revisiting Thomson’s model with multiply charged superfluid helium nanodroplets

We study superfluid helium droplets multiply charged with Na+ or Ca+ ions. When stable, the charges are found to reside in equilibrium close to the droplet surface, thus representing a physical realization of Thomson's model. We find the minimum radius of the helium droplet that can host a given number of ions using a model whose physical ingredients are the solvation energy of the cations, calculated within the helium density functional theory approach, and their mutual Coulomb repulsion energy. Our model goes beyond the often used liquid drop model, where charges are smeared out either within the droplet or on its surface, and which neglects the solid-like helium shell around the ions. We find that below a threshold droplet radius R0, the total energy of the system becomes higher than that of the separated system of the pristine helium droplet and the charges embedded in their solvation microcluster ("snowball"). However, the ions are still kept within the droplet by the presence of energy barriers, which hinder Coulomb explosion. A further reduction of the droplet radius below a value Rexpl eventually results in the disappearance of such barrier, leading to Coulomb explosion. Surprisingly, our results are rather insensitive to the ion atomic species. This makes room to discuss them in the context of intrinsic multicharged helium droplets, where the charges are triatomic He3+ ions. Our calculated values for Rexpl display the correct scaling with the number of cations compared to the available experimental results, at variance with other estimates for the critical radii.