  We present numerically exact solutions to the problem of a single electron
interacting through a long range interaction with optical phonons in two and
three dimensions. Comparisons are made with results for the standard Holstein
model, and with perturbative approaches from both the weak coupling and strong
coupling sides. We find, in agreement with earlier work, that the polaron
effective mass increases (decreases) in the weak (strong) coupling regime,
respectively. However, in two dimensions, the decrease in effective mass still
results in too large an effective mass to be relevant in realistic models of
normal metals. In three dimensions the decrease can be more relevant, but
exists only over a very limited range of coupling strengths.
