On an adiabatic approach in the theory of electron-ripplon scattering at a liquid helium surface

The problem of electron-ripplon scattering on a liquid helium surface is investigated by using the Born- Oppenheimer adiabatic principle. The results obtained permit determination of the validity of different approaches to the description of electron-ripplon interaction which are encountered in the literature. It is shown that because of the strong coupling between the electrons and the helium surface, taking account of adiabaticity in a direction perpendicular to the liquid-vapor interface is most important in the problem of electron-ripplon scattering. After this adiabaticity has been taken into account the Bloch and Born- Oppenheimer approaches yield the same result for the motion in the plane of the liquid-vapor interface. Without taking account of adiabaticity in the Z coordinate, these approaches lead to substantially different results.

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