  The intermediate coupling regime in polaronic systems, situated between the
adiabatic and the anti-adiabatic limit, is characterized by resonant pairing
between quasi-free electrons which is induced by an exchange interaction with
localized bipolarons. The onset of this resonant pairing takes place below a
characteristic temperature T* and is manifest in the opening of a pseudogap in
the density of states of the electrons. The variation of T* is examined here as
a function of (i) the typical frequency \omega_0 of the local lattice modes,
which determines the binding energy of the bipolarons, and (ii) the doping,
which amounts to a relative change of the bipolaron concentration n_B to that
of the free electrons n_F. We concentrate on a doping regime, where small
changes in doping give rise to a large change in T*, which is the case when n_B
is small (< 0.1 per site). For finite values of n_B we find negative and
practically doping independent values of the isotope coefficient \alpha^* which
characterizes the formation of resonating electron pairs. Upon decreasing the
total particle density such that n_B becomes exponentially small, we find a
rapid change in sign of \alpha^*. This is related to the fact that the system
approaches a state which is more BCS-like, where electron pairing occurs via
virtual excitations into bipolaronic states and where T* coincides with the
onset of superconductivity.
