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

TL;DR

This paper proposes a new fitting function for the critical Casimir force in $^4$He films below the lambda point, which aligns better with experimental data than previous mean field models.

Contribution

The authors extend a mean field calculation to derive an approximate scaling function that fits experimental results more accurately.

Findings

The proposed fitting function matches experimental data better in three dimensions.

The extrapolated scaling function is similar to experimentally obtained functions.

The new function improves upon previous mean field results.

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].