157 4.08 s O> 4.o4 4.oo -/ 1 ' P = 2.oo x 10 22 /cm 3 ooxosxD J 1 1 J ! J Thickness D in A

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. I t is found that the model predicts a shift of the specific-heat maxima to higher temperatures a s 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.

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The properties of liquid helium in thin film geometry are studied using both the ideal Bose–Einstein gas and the hard-sphere gas as models. Of particular interest is the occurrence of a statistical correlation length which has roughly the same value in both models and which may help explain some recent experimental results on the behavior of liquid helium in thin films and pores. The limitations of the methods used for the interacting gas are discussed in some detail.

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