Bound states of an electron in an impurity potential on the surface of liquid helium

The energies and widths of the levels of an electron on impurity centers on the surface of liquid helium are calculated with allowance for the deformation of the surface. The level shift associated with the deformation effects is small and decreases very slowly with increasing level number. However, even a small shift of the energy levels relative to one another affects ripplon scattering, which makes the main contribution to the level width at low temperatures. It is predicted theoretically that this width depends very strongly on the external parameters and on the level number and that a maximum obtains at a clamping field E⊥=51500 V/cm. The width of the levels of an electron in a bound state is found to be less than for free electrons. This makes it possible to perform a beautiful spectroscopic experiment.