LIQUID HELIUM AND THE PROPERTIES OF FINITE BOSE–EINSTEIN ASSEMBLIES

In order to explain certain properties of thin helium films, Ziman has proposed an ideal gas model in which the bulk liquid is treated as a collection of independent, Bose–Einstein assemblies each a few hundred angstroms in extent. In this paper, an extensive numerical study is made of the thermodynamic properties of such finite assemblies. In particular, the specific heats of thin films have been calculated on the basis of the model and the results compared with the experimental data of Frederikse. It is found that the model predicts a shift of the specific-heat maxima to higher temperatures as the film thickness is decreased, rather than to lower temperatures as required by the observations on actual helium films. The nature of the Bose–Einstein condensation in finite assemblies is discussed in some detail and some general conclusions are drawn concerning Ziman's model.