Energy spectrum of surface electrons over the 3He–4He solution film with inhomogeneous isotope distribution

Abstract

The energy spectrum of surface electrons localized over a 3He–4He liquid solution film covering a solid substrate is theoretically determined using the variational method. Two models of the spatial distribution of helium isotopes over the film height are considered. In one of them, it is believed that the film is stratified, and a continuous linear change in concentration is assumed in the second one. The potential energy of an electron is determined by the method of solving the Poisson equation for the electrostatic potential and in the gas approximation. Furthermore, it is established that the results of both methods practically coincide for a stratified film. The dependence of the energy gap between the ground and first excited states of surface electrons as a function of the film thickness is determined. Comparison of the results for the considered models of the film structure is carried out. The possibility of using the results obtained in an experimental study of the spatial isotopic distribution in a helium solution by the neutron scattering method is discussed.The energy spectrum of surface electrons localized over a 3He–4He liquid solution film covering a solid substrate is theoretically determined using the variational method. Two models of the spatial distribution of helium isotopes over the film height are considered. In one of them, it is believed that the film is stratified, and a continuous linear change in concentration is assumed in the second one. The potential energy of an electron is determined by the method of solving the Poisson equation for the electrostatic potential and in the gas approximation. Furthermore, it is established that the results of both methods practically coincide for a stratified film. The dependence of the energy gap between the ground and first excited states of surface electrons as a function of the film thickness is determined. Comparison of the results for the considered models of the film structure is carried out. The possibility of using the results obtained in an experimental study of the spatial isotopic distribution in...