Critical casimir force in ⁴He films: Confirmation of finite-size scaling

We present new capacitance measurements of critical Casimir force-induced thinning of ⁴He films near the superfluid transition, focused on the region below T_λ where the effect is the greatest. ⁴He films of 238, 285, and 340 Å thickness are adsorbed on atomically smooth, N-doped silicon substrates. The Casimir force scaling function ν, deduced from the thinning of these three films, collapses onto a single universal curve, attaining a minimum ν = -1:30 ± 0:03 at x = td^1/ν= - 9:7 ± 0:8 Å ^1/ν. The collapse confirms the finite-size scaling origin of the dip in the film thickness. Separately, we also confirm the presence down to 2.13 K of the Goldstone or surface fluctuation force, which makes the superfluid film ∼2 Å thinner than the normal film.