Energy spectrum of surface electrons over a 3He - 4He solution with a spatially non-uniform distribution of the light isotope

The energy gap between the ground and first excited energy levels of surface electrons deposited over a dilute 3Не - 4Не solution is evaluated. Two spatial distributions of 3Не atoms near the free surface solution are considered. One consists of a thin though macroscopic 3Не film and in the other the 3Не concentration varies continuously from the surface inside the liquid. The energy gap is calculated as a function of the parameters of the 3Не spatial distribution for these distributions. It is shown that the energy gap dependence on the distribution parameters allows using measurements of intersubband transitions of the surface electrons to determine the 3Не concentration distribution and, in principle, the nature of the spatial distribution of the light isotope near the surface of the solution.