  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.
