LVIII. Bose-Einstein condensation in helium films

Abstract

It is shown that an ideal Bose-Einstein gas confined to a layer of any finite thickness behaves like a ‘two-dimensional gas’ in that the temperature of the B.E. condensation is size dependent and tends to zero as the area of the layer tends to infinity. Such an effect is not observed in real helium films. If it is assumed that liquid He must be treated as if made up of independent B.E. assemblies, each smaller than a fixed length L ₀ (∼ 7 × 10^-6 cm), the observed variation, with thickness, of the temperature of onset of superfluidity, in unsaturated films, may be closely predicted. The zero-point motion in each restricted assembly is then close to the critical transfer velocity of superflow, and L ₀ is of the same order of magnitude as the thickness of the saturated film. This assumption brings the ideal B.E. gas model nearer to the real structure of liquid He, but the interpretation of L ₀ as a ‘scattering length’ does not give agreement with estimates from kinetic theory.