The motion of electrons parallel to the surface of a liquid-helium film on a sapphire substrate is described by a Fr\"ohlich-type Hamiltonian of the polaron. The polaronic transition from the nearly free to a quasilocalized state is observed at a certain critical value of the film thickness. We have pointed out situations in which a dimple filled with several electrons could be trapped at the helium film.
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Degani et al. (1985) studied this question.
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