Pseudogap Phenomena in the BCS Pairing Model

We investigate pseudo-gap phenomena realized in the BCS pairing model with a long but finite interaction range. We calculate the single-particle self-energy in all order exactly in the temperature range where the superconducting fluctuation propagator is Gaussian-like. It is found that vertex corrections to the self-energy which are discarded in the previous studies are crucially important for the pseudo-gap of the single-particle density of states in higher order calculations.