  Zero temperature crossover from superfluidity to superconductivity with
carrier density increasing is studied for a two-dimensional system in the
s-wave and d-wave pairing channels. It was assumed that the particle attraction
correlation length depends on carrier density $n_f$ as $r_0\sim1/\sqrt{n_f}$.
Such a dependence was found experimentally for the radius of magnetic
correlations in $La_{2-x}Sr_xCuO_4$. The short range Coulomb repulsion was also
taken into account. It is shown that the behaviour of the system with doping is
fundamentally different from the case with $r_0(n_f)=const$. In particular,
similarly to the d-wave case, the crossover in the s-channel takes place only
if the coupling is larger of some minimal value, otherwise the Cooper pairing
scenario takes place at any small carrier density. The relevance of the model
to high-temperature superconductors is discussed.
