Theory of surface excitations of liquid helium four

Abstract

The wavefunction proposed by Chang and Cohen (see Phys. Rev. B, vol.11, p.1059 (1975)) for surface excitations of a quantum fluid is used to calculate the excitation energy epsilon (k). A general relation epsilon (k)<or=h(cross)2k2/2mS*(k) is obtained, where S* (the surface structure factor) is determined in terms of the density profile and the pair correlation function. If one assumes that the liquid has bulk properties right up to the surface, the theory leads rigorously to epsilon (k)= pi h(cross)ck/(ln(2/ka)+constant) in the long wavelength limit. This expression is in qualitative agreement (for intermediate values of k) with the semiclassical theory of Edwards, Eckardt and Gasparini, and with the numerical work of Chang and Cohen. The authors discuss the proposal that the inclusion in the groundstate of correlations due to the zero-point motion of the surface modes would lead to the classical dispersion relation epsilon approximately k32/.