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 ³He - ⁴He solution is evaluated. Two spatial distributions of ³He atoms near the free surface solution are considered. One consists of a thin though macroscopic ³He film and in the other the ³He concentration varies continuously from the surface inside the liquid. The energy gap is calculated as a function of the parameters of the ³He 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 ³He concentration distribution and, in principle, the nature of the spatial distribution of the light isotope near the surface of the solution.