  We have introduced a Coulomb correlated normal state to study the
superconducting pairing with a Fermi liquid like normal phase background in a 3
dimensional system. The role of the Coulomb correlation has been actively
incorporated by means of Gutzwiller projection scheme, in the presence of
phonon mediated attractive electron-electron interaction throughout the entire
regime of its applicability. We variationally modulate the Coulomb correlation
strength from the weak to the strong regime in our calculational procedure. The
main highlight of our results is the appearance of a '2-gap-like' structure in
the superconducting phase, arising out of the two-body interacting matrix
elements, calculated in the presence of the active Coulomb correlation. We have
made use of the 'two-square well model' potential to evaluate the
superconducting pairing gaps at zero temperature. Our Calculational scheme has
been applied to a simple cubic lattice system for a physical realization. All
the consequences are elaborated and discussed.
