Surface tension of helium at the superfluid critical end-point

Abstract

The singularity in the vapor-liquid interfacial tension, ∑(T), of helium at the transition to superfluidity is analyzed theoretically. The universal amplitude ratio R σξ + =K+(ξ 0 + )d−1/k B Tλ , where K+ and K− are the amplitudes of the |T−Tλ|µ singularity in ∑, with μ=1.34 3 , is known from recent work to first order in e=4−d for the general n-vector model in d dimensions. Extrapolation to d=3 for n=2 indicates R σξ + =0.05−0.08, which is shown to be consistent with the experimental data. Further analysis of the experiments establishes that the universal ratio Q=K+/K − exceeds 0.35, and is consistent with the recent prediction Q≃0.9; this demonstrates the inadequacies of earlier theoretical treatments. The existence in the observed surface tension of an anomalous, negative contribution of unknown origin at a few millikelvin beneath Tλ is stressed.