The behaviors of helium films are expected not to be in accordance with that of bulk fluid. Our theories are based on Husimi's quantum statistical effect, by which surface effect is added as a correction to the ordinary theory. We calculate temperature T as a function of α numerically, the latter is a parameter to be determined by the number of particles.
We obtain energy, entropy and specific heat as a function of T. When the width is narrow enough, for appropriate boundary condition, our curve is in good agreement with that of Toda & Takano, derived by grand partition function method.
For actual liquid helium, we introduce Δ. ν modification and our curves of specific heat are not shifted so much compared with bulk one, instead of taking the width narrow, so the agreement of this theory with experiment is not expected. But the reduction of transition temperature is capable to be in agreement with experiment, by the correction of surface density.
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