Surface excitations and surface tension of superfluidHe4

The Atkins theory of the temperature dependence of the surface tension $\alpha$ in superfluid ${\mathrm{He}}^4$ has been improved by including the effects of compressibility, phonon dispersion, and Gibb's "surface adsorption" or "surface mass" in the calculation of the spectrum of the surface excitations or "ripplons." The theoretical ripplon spectrum is found to have a minimum close to the roton minimum in the empirical phonon spectrum. The results of the theory, which should be accurate up to a temperature of ∼1.3 K, are presented in terms of the ripplon and phonon contributions to the surface entropy ($-\frac{d\alpha }{dT}$). The ripplon spectrum and the surface entropy are found to depend on two phenomenological parameters: a length $\delta$ which is the surface mass per unit area divided by the density, and an area $a$ which is the derivative of $\delta$ with respect to the curvature of the surface. In principle, both $\delta$ and $a$ can be obtained from static measurements on curved surfaces. The theory is compared to new measurements of the surface entropy near 1 K and, assuming that $\delta$ is small, $a$ is found to be about 1.5${\mathrm{\AA }}^2$.