Abstract: The pairing instability induced by either a givenattractive interaction or particle-hole excitations isexamined by using the perturbational diagram approach.A graphical functional derivative method based onWard's identity is developed to represent thecontributions to the interparticle interactions fromdifferent channels. It is shown that pairinginstability for the electrons excited from the Fermisea may happen due to the presence of holes even whenthe original interaction is repulsive. Thus, incontrast to the Cooper instability caused by a givenattractive interaction, the pairing instability can beinduced by the particle-hole excitations. Thescattering diagrams from this model allows one toevaluate the two particle vertex function and T$-c$/ byusing the pole condition of the vertex function. It hasbeen found that T$- c$/ can reach quite high values andgives rise to the bell shape. The application of theresults to a layered 2D Fermi gas is considered. !18
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