Surface Levels and Their Contribution to the Surface Tension of Quantum Liquids

We investigate the new type of excitations on a liquid surface, which were proposed in A.M. Dyugaev, P.D. Grigoriev (JETP Lett. 78:466, 2003) to explain the long-standing puzzle of the strong temperature dependence of the surface tension coefficient of liquid helium. These excitations, called surfons, appear because helium atoms have discrete energy level at the liquid surface, being attracted to the surface by the van der Waals force and repulsed at a hard-core interatomic distance. The surfons propagate along the surface and form a two-dimensional gas. The concentration of the surfons increases with temperature. Basing on the simple quantum-mechanical model of the surfon microscopic structure, we estimate the surfon activation energy and effective mass for both helium isotopes. We also calculate the contribution of the surfons to the temperature dependence of the surface tension, taking into account the experimental temperature dependence of the chemical potential of liquid helium. This allows to achieve very high agreement between our theory and experiment on the temperature dependence of surface tension from zero to almost boiling temperature and to determine the contribution of ripplons. This temperature dependence is quadratic in a wide temperature interval for both helium isotopes. The comparison with experiment allows to extract the surfon activation energy and effective mass. The values of these surfon microscopic parameters agree with the values, calculated from the proposed microscopic model of surfon structure.