Jury members
A.F. Borghesani, T. Belmont, H. Glyde, C. Baudet, J. Roudet, N. Bonifaci

Abstract
Electrons and positive ions are microscopic probes frequently used to explore transport, diffusion and quantum prope rties of liquid helium. Electrons introduced into liquid helium localise and build large cavities with radii up to 20 Å (at 4.2 K and 1 bar), depending on the pressure. The formation of such voids results from the repulsive interaction between ground state helium atoms and electrons because of the Pauli principle and the very long range van der Waals-like attraction. Positive ions in liquid helium behave the opposite way. In this case, electrostrictive forces between the positive charge and the surrounding polarised helium atoms dominate and attract the helium atoms towards the positive centre. As a consequence a dense, solid-like shell of helium is built, which is why the term ’Atkins-snowball’ is often used. Information of the size that electrons and ions occupy in helium is difficult to obtain in a direct fashion. On the contrary, thanks to the charged nature of electrons and ions, the measurement of their mobility is relatively straightforward to measure using electric fields. The mobility is related to a hydrodynamic radius r via the well known Stokes law for spherical objects and the deduction of the radius requires no other knowledge than the viscosity, of the fluid. A number of restrictions nevertheless apply. In particular at low densities where Knudsen number are greater than one the more general Millikan-Cunningham equation must be used instead of Stokes law. Finding a coherent description of ion and electron mobility in different density regions, especially the crossover from gas kinetic to Stokes flow is a challenge. An implicit challenge is that ions and electrons in helium are expected to change their structure depending on the density. We develop thermostatic state equations for electrons and He ions in helium and employ the free volume model to derive the hydrodynamic radius. In general terms, the free volume model relates the size of foreign objects, i.e. solute molecules within a fluid to the size occupied by a free volume unit cell, (V-b)/N, using as the first approximation a simple power law between the two. The state equations of P, V and T include parameters which are calibrated using experimentally determined mobilities reported in the literature. The mobilities, are related to the size via the hydrodynamic radius, in the Stokes-Einstein equation and by introducing the Millikan-Cunningham factor specifically developed for electrons and ions in helium to account for a large density coverage of our thermodynamic approach, including the gas, supercritical, liquid and superfluid phases.