Proposed fitting function for the critical Casimir force on $^4$He film below the $\lambda$ point

Abstract

We have extended the mean field calculation of Zandi et al [1] and have obtained an approximate mathematical expression for the Casimir scaling function, which if extrapolated to the domain $\pi^2\ge-y\ge 0$, becomes surprisingly similar to that obtained experimentally by Ganshin et al [2]. The extrapolated scaling function can be regarded as a proposed fitting function, that appears to agree better with the experiments [2] in D=3, than the exact mean field result of Zandi et al [1].