Journal of Low TemperaturePhysics, Vol.83, Nos, 5/6, 199l 3He Impurity States on Liquid 4He: From Thin Films to the Bulk Surface N. Pavloff and J. Treiner Division de Physique Th~orique,* Institut de Physique Nucl~aire, Orsay, France (Received September 20, 1990, revised February 25, 1991) The structure of the states accessible to 3He impurities in films of liquid 4He on Nuclepore is investigated using a density functional approach with a finite- range effective interaction. In thick films, one finds that the two lowest states are localized in the surface region. For thinner films, the variation with film thickness of the first three states results from a delicate balance between the attractive tail of the substrate potential and the quantum finite-size effect. The existence of states localized in the second layer of the films is discussed. The energy difference between the ground state and the first excited state agrees with the recent determination of Higley, Sprague, and Hallock from magnetiz- ation measurements. The effective mass of the ground state has a structure similar to that obtained by Krotscheck and coworkers and exhibits a maximum for a 4He coverage 0f0.15 A -2, in agreement with the data of Gasparini and coworkers. A similar behavior is predicted for the effective mass of the first, second, and third excited states. The structure of the energy spectrum may also explain former results on third-sound measurements in thin mixture films by Laheurte et al. and by Hallock. 1. INTRODUCTION Much experimental and theoretical work has been devoted to the study of 3He impurities on liquid 4He. As originally proposed by Andreev, 1 3He impurities in the bulk liquid are localized on the surface, and in a series of beautiful experiments, Edwards and coworkers2 have confirmed the behavior of a two-dimensional Fermi gas (2DFG), built on a ground state with energy -5 K and characterized by an effective mass in the range 1.30-1.45 times *Unit6 de Recherche des Universitrs Paris 11 et Paris 6 associre au CNRS. 331 0022-2291/91/0600-0331506~50/0 © 1991Plenum Publishing Corporation