  Cooper's formalism for fermionic pairing has been revisited considering upto
3rd neighbour hopping terms, firstly with a Fermi liquid like background on a
square lattice keeping in mind the overdopped cuprates. Then the whole scheme
is repeated with a Marginal Fermi liquid- like background, taking into account
the self energy correction of the mobile electrons to include a more realitic
density of states in the calculation. Detailed comparison of our theoretical
results with those from experiments strongly supports the Marginal Fermi
liquid- like character of the normal phase with exciton mediated
superconducting pairing in the concerned materials, in the lightly overdoped
phase.
