Analytic structure of long-wavelength excitations in⁴He surfaces

We study the analytic structure of the static structure function, the pair distribution function, and the direct correlation function in Bose liquid surfaces for films of finite thickness adsorbed to a plane substrate and also for the case of an infinite half space. In the longwavelength limit it is shown, in the first case, that these functions behave essentially as in two-dimensional systems, whereas the structure function of an infinite halfspace consists of two zero-frequency components corresponding to contributions from the ripplon and the phonon excitations. Explicit representations for the states are given for both cases.