Theory of the resonant properties of electrons localized on the surface of liquid helium

The problem of the shape of the line of optical transition of an electron between bound states on the surface of liquid helium is solved within the independent boson model. Such bound states are realized, for example, in the potential of a positively charged impurity located on a substrate or in the field of a He⁺ ion located beneath the surface. Reference is made to the importance of the relaxation processes of the dimple on the helium surface under the electron. The adiabatic approximation, in the case of which the dimple does not change during the time of electron transition, is not always valid. At low temperatures, two maxima may appear on the absorption line. It is demonstrated that the far tails of the optical absorption line feature a universal (Urbach rule) exponential dependence on the electron transition energy.