  This work present a new class of variational wave functions for fermi systems
in any dimension. These wave functions introduce correlations between Cooper
pairs in different momentum states and the relevant correlations can be
computed analytically. At half filling we have a ground state with critical
superconducting correlations, that is argued to be exact for the model
considered. We find large enhancements in a Cooper pair correlation function
caused purely by the interplay between the uncertainty principle, repulsion and
the proximity of half filling. This is surprising since there is no
accompanying signature in usual charge and spin response functions, and
typifies a novel kind of many body cooperative behaviour.
