  The tunneling probability between two leads connected by a molecule, a chain,
a film, or a bulk polarizable insulator is investigated within a model of an
electron tunneling from lead A to a state higher in energy, describing the
barrier, and from there to lead B. To describe the possibility of energy
exchange with excitations of the molecule or the insulator we couple the
intermediate state to a single oscillator or to a spectrum of these,
respectively. In the single-oscillator case we find for weak coupling that the
tunneling is weakly suppressed by a Debye-Waller-type factor. For stronger
coupling the oscillator gets 'stiff' and we observe a suppression of tunneling
since the effective barrier is increased. The probability for the electron to
excite the oscillator increases with the coupling. In the case of a film, or a
bulk barrier the behavior is qualitatively the same as in the single oscillator
case. An insulating chain, as opposed to a film or a bulk connecting the two
leads,shows an 'orthogonality catastrophe' similar to that of an electronic
transition in a Fermi gas.
