  Transport through molecular quantum dots coupled to a single vibration mode
is studied in the case with strong coupling to the leads. We use an expansion
in the correlation between electrons on the molecule and electrons in the leads
and show that the tunneling broadening is strongly suppressed by the
combination of the Pauli principle and the quantization of the oscillator. As a
consequence the first Frank-Condon step is sharper than the higher order ones,
and its width, when compared to the bare tunneling strength, is reduced by the
overlap between the groundstates of the displaced and the non-displaced
oscillator.
