Comment on the Specific Heat of a Bose Gas Confined to a Thin-Film Geometry

Our previous evaluation of the specific heat of an ideal Bose gas confined to a thin-film geometry is extended to second order in ($\frac{\overline{l}}{D}$), where $\overline{l}$ is the mean interparticle distance. Explicit expressions, involving a dimensionless parameter $y$, are obtained both for the specific heat of the system and for the temperature at which the specific heat is maximum. Occurrence of the parameter $y$, which is a measure of the chemical potential of the system in terms of the spacing of the single-particle energy levels, enables us to cast our expression for the specific heat of the system into a form consistent with the scaling theory of Fisher and Barber. Our results for the specific-heat maximum, as a function of ($\frac{D}{\overline{l}}$), are a considerable improvement over the first-order ones reported earlier, and have come remarkably close to the ones obtained numerically by Goble and Trainor.