Energy spectrum of surface electrons over the 3He–4He solution film with inhomogeneous isotope distribution
E.S. Sokolova and S.S. Sokolov
B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine 47 Nauky Ave., Kharkiv 61103, Ukraine
Received June 25, 2018, published online November 26, 2018
Theoretically, using the variational approximation, the energy spectrum of surface electrons localized above the film of the liquid solution of 3Не–4Не covering the solid-state substrate is determined. Two models of the spatial distribution of helium isotopes along the height of the film are considered. In one of them it is assumed that the film is stratified, in the second one, continuous linear change of concentration is supposed. 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, and a practical coincidence of the results of both methods for the stratified film is established. The dependence of the energy gap between the ground and first excited states of surface electrons as a function of the thickness of the film is de-termined. The results for the considered models of the film struc-ture are compared. The possibility of using the obtained results for an experimental study of the spatial isotopic distribution in a helium solution by the neutron scattering method is discussed.
Key words: solution 3Не–4Не, stratification of solution, helium film, surface electrons.