Extending the Fr\"ohlich polaron problem to a discrete ionic lattice we study a polaronic state with a small radius of the wave function but a large size of the lattice distortion. We calculate the energy dispersion and the effective mass of the polaron with the 1/λ perturbation theory and with the exact Monte Carlo method in the nonadiabatic and adiabatic regimes, respectively. The ``small'' Fr\"ohlich polaron is found to be lighter than the small Holstein polaron by 1 or more orders of magnitude.
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Alexandrov et al. (1999) studied this question.
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