HE-3 IMPURITY STATES ON LIQUID-HE-4 - FROM THIN-FILMS TO THE BULK SURFACE

The structure of the states accessible to He-3 impurities in films of liquid He-4 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 magnetization 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 He-4 coverage of 0.15 angstrom-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.