  We use both a perturbative Green's function analysis and standard
perturbative quantum mechanics to calculate the decrease in energy and the
effective mass for an electron interacting with acoustic phonons. The
interaction is between the difference in lattice displacements for neighbouring
ions, and the hopping amplitude for an electron between those two sites. The
calculations are performed in one, two, and three dimensions, and comparisons
are made with results from other electron-phonon models. We also compute the
spectral function and quasiparticle residue, as a function of characteristic
phonon frequency. There are strong indications that this model is always
polaronic on one dimension, where an unusual relation between the effective
mass and the quasiparticle residue is also found.
