A new model for the density-dependence of positive ion mobility in liquid helium

The free volume model has in the past been used to calculate ionic conductivities of liquids and solids successfully. We have recently applied this method to calculate electron mobilities and electron cavity radii in liquid and supercritical helium. A key step in our approach is the development of van der Waals-type state equation with an appropriately chosen expression for the internal pressure describing the attraction between fluid and impurities. Here we develop this approach further to study positive ions. We find for positive ions a much simpler form of the internal pressure than for electrons. The ion mobility calculated with our method for pressures between 1 and 100 bar agree very well with experimental data recorded at 2.2, 3 and 4.2 K. The radii associated with mobility values vary from 0.55 nm to 0.4 nm with pressure or density. In liquid helium, positive ions form `Atkins´ snowballs, a structure in which a positive core attracts the helium atoms from its solvation shell to form a densely, solid-like packed layer. The helium density profile of this interface is much sharper than for electron cavities in helium and gives rise to a lower compressibility of the positive impurity. We believe that this sharper density profile is the reason for the much simpler form of the internal pressure than for electrons.