On the Problem of Unsaturated Helium Films

A theoretical explanation is given for the lowering of the transition temperature, and the increase of the entropy, with decreasing film thickness as met with in unsaturated helium films. It is shown that in the ideal gas approximation the boundary conditions obeyed by the eigenfunctions assume rather an important role. There is, however, no quantitative agreement between the experimental and the theoretical results even when the dependence of the film density on the thickness of the film is taken into account. On the other hand, if one considers the non-ideal gas approximation for the liquid and takes into account (i) the slow variation of the parameters J and p. with the film thickness, and (ii) the contributions arising from the presence of surface tension waves on the liquid surface, the experimental data are explained in a good quantitative manner. In this case, however, the boundary conditions are found to become rather unimportant