The properties of the electron-ripplon system on the surface of liquid helium film influence the properties of liquid helium very markedly.The problem of a two-dimensional electron on the surface of a liquid helium film was formulated by Jackson and Platzaman as a surface polaron problem.The properties of eleron-ripplon system on the surface of liquide helium film have been of considerable interest.The surface polaron in the eletron-ripplon system is investigated by Tokuda within the modified variational scheme of the Lee-Low-Pines theory which is valid for the whole range of the eletron-ripplon coupling.Jackson and Peeters have applied and extension of the Feynman path-integral formalism to the problem of noninteracting polaronic electron on the surface of a liquid helium film in a perpendicularly applied magnetization field.The ground state energy

the Feynman-model mass

the magnetization

and susceptibility of the system are calculated.The Landau-pekar variational theory for investigating the strong-coupling system of electron-phonon in crystals is employed by Jin Pei-wan et al.to study the system of an electron strongly coupled to ripplons on the outer surface of the liquid-helium film.Analytical expressions of the ground state energy

the effective mass

and the average number of virtual ripplons around the electron are obtained.Huybrechts proposed a linear combination operator method

by which a strong-coupling polaron was investigated.On the basis of Huybrechts' work

Tokuca added another variational parameter to the momentum operator and also evaluated the ground-state energy and effective mass of the bulk polaron.In fact

so far research on the electron-ripplon system has been restricted to approximation and calculation where the interaction between ripplons of different wave vectors in the recoil process in neglected.The properties of the surface magnetopolaron and the surface polaron

considering the corresponding interaction

have been discussed by the present authors.The effect of the interaction between ripplons of different wave vectors in he recoil process on the effective mass of the electron-ripplon system are studied by using linear combination operator and pertur-bation method in this paper.