  The polaron features due to electron-phonon interactions with different
coupling ranges are investigated by adopting a variational approach. The
ground-state energy, the spectral weight, the average kinetic energy, the mean
number of phonons, and the electron-lattice correlation function are discussed
for the system with coupling to local and nearest neighbor lattice
displacements comparing the results with the long range case. For large values
of the coupling with nearest neighbor sites, most physical quantities show a
strong resemblance with those obtained for the long range electron-phonon
interaction. Moreover, for intermediate values of interaction strength, the
correlation function between electron and nearest neighbor lattice
displacements is characterized by an upturn as function of the electron-phonon
coupling constant.
