Excitation spectrum of the vapor-liquid 4He interface.

Abstract

We analyze the elementary excitations in a vapor-liquid $^{4}\mathrm{He}$ interface with planar symmetry under saturation conditions. They are characterized by a momentum \ensuremath{\Elzxh}q parallel to the interface plane and may be described by bound or continuum states. The wave functions of bound states are confined to the interface region. The continuum states may be described by their properties in the asymptotic region far apart from the interface layer. There, they are representing plane waves with momentum \ensuremath{\Elzxh}${\mathbf{q}}_{\mathit{L}}$ and/or \ensuremath{\Elzxh}${\mathbf{q}}_{\mathit{V}}$ vertical to the interface plane. The dispersion of these waves is determined by the energy-momentum relation in bulk liquid or vapor $^{4}\mathrm{He}$. We may distinguish liquid, vapor, or vapor-liquid continuum states. The wave functions and energies are numerically evaluated in a generalized Feynman approximation, at various temperatures, 0\ensuremath{\le}T\ensuremath{\le}2 K. At nonvanishing temperatures, the wave functions of bound states represent rotons with wave number q\ensuremath{\simeq}${\mathit{q}}_{\mathit{R}}$=1.8 \AA{} $^{\mathrm{\ensuremath{-}}1}$ trapped in the interface layer. At zero temperature, bound states appear at any wave number 0.2 \AA{} $^{\mathrm{\ensuremath{-}}1}\mathit{q}_{\mathit{R}}$ describing excitations of the free $^{4}\mathrm{He}$ surface. At temperatures 0T\ensuremath{\le}1.5 K, the numerical results show that there are resonant vapor continuum states that have a very small amplitude in the asymptotic vapor region but develop an anomalously large amplitude in the interface layer. Our results on the excitation energies and on the corresponding wave functions in the interface region are displayed in a series of figures and are discussed in detail.