  Cooper's one pair problem is investigated for a 2D lattice in the background
of both passive and active Fermi sea in a weakly correlated environment. Boson
exchange mechanisms involving excitons as well as phonons are invoked for
pairing in the s- wave channel. The important quantities calculated are pairing
energy and coherence length as functions of bosonic energy, attracted coupling
constant and band filling factor. Comparison of our theoretical results with
those from experiments on overdoped cuprate superconductors and other type of
theoretical calculations show electronic mechanism to be the more likely
mechanism of pairing in the overdoped phase.
