Interaction of negative ions with the surface of inert liquids

The interaction potential of negative ions (electron bubbles) with the surface of liquid ⁴He, ³He, and Ne has been found. In addition to the electrostatic repulsion, the contribution of the long-range Van der Waals attraction of the electron bubble to the liquid surface has been also taken into account. Competition of these repulsion and attraction forces results in the formation of a potential barrier that prevents the motion of a negative ion from the liquid to the vacuum. The temperature and electric-field dependences of the lifetime of the bubble have been determined. The theory has been compared with the experiments with negative ions in liquid ⁴He. In contrast to the conventional idea based on the hypothesis of the quantum tunneling of an electron from a bubble to a vacuum, our theory is based on the Kramers’ diffusion model of the classical escape of the bubble over the potential barrier. In this model, a low-dynamic-friction approximation is applicable to liquid ⁴He owing to a high mobility of negative ions in the superfluid.