Properties of bound, resonant, and regular continuum states of the excitation spectrum of symmetric liquid 4He films at T=0 K.

Abstract

Elementary excitations in rather thick symmetric films of liquid {sup 4}He at {ital T}=0 K are investigated. They are characterized by a momentum {h_bar}{ital q} parallel to the surface and may be described by bound or continuum states, which are obtained by solving a Bogoliubov-type equation formulated within the framework of the paired-phonon analysis and the hypernetted-chain approximation. Films of coverages {ital n}{sub {ital c}}=0.3 and 0.4 A{sup {minus}2} confined by simple Gaussian potentials are studied. The excitation spectrum is numerically evaluated by discretizing the associated eigenvalue problem in a finite box. The evolution of the energy levels as a function of the box size is explored. Examples of the calculated energies and wave functions are displayed in a series of figures. Two differing sorts of continuum states may be distinguished. Depending on the behavior of their excitation energies as a function of the box size on the one hand, and the spatial distribution of their wave functions inside the film and in the asymptotic region far apart from the interface layer on the other, the continuum solutions can be separated into two classes of excitations: (a) the {open_quote}{open_quote}regular{close_quote}{close_quote} continuum states and (b) the {open_quote}{open_quote}resonant modes.{close_quote}{close_quote} The matrix elements ofmore » the particle-hole potential and the penetration factors of the most important states are examined. The lowest-lying branch of states is always bound and for {ital q}{lt}{ital q}{sub {ital R}} ({ital q}{sub {ital R}}{approx_equal}1.9 A{sup {minus}1} being the momentum at the roton minimum) it describes surface ripplon excitations. In the atomic scale regime, 1.1 A{sup {minus}1}{lt}{ital q}{lt}{ital q}{sub {ital R}}, the hardest {open_quote}{open_quote}resonant mode{close_quote}{close_quote} can be interpreted as a roton trapped at the center of the film and therefore associated with bulk excitations of the system.« less