In this paper, taking into account the effect of the induced interaction, we calculate the superfluid-transition temperature of ultracold Fermi gases within the framework of the non-self-consistent
T-matrix approximation. The result shows that the transition temperature is reduced by about
10 at unitarity due to the induced interaction. In the Bardeen-Cooper-Schrieffer (BCS) limit, the critical temperature is about
0.45TcBCS and it is the same as the result of the usual Gorkov and Melik-Barkhudarov correction, whereas in the Bose-Einstein condensate (BEC) limit, the influence of the induced interaction can be neglected and the critical temperature turns out to be the transition temperature of ideal Bose gases. Our results show that the induced interaction cannot be neglected in the study of the BCS-BEC crossover.
Analytical expressions are given for the static structure factor S(k) and the pair correlation function g(r) for uniform ideal Bose‐Einstein and Fermi‐Dirac gases for all temperatures. In the vicinity of Bose Einstein condensation (BEC) temperature, g(r) becomes long ranged and remains so in the condensed phase. In the dilute gas limit, g(r) of bosons & fermions do not coincide with Maxwell‐Boltzmann gas but exhibit bunching & anti‐bunching effect respectively. The width of these functions depends on the temperature and is scaled as √ (inverse atomic mass). Our numerical results provide the precise quantitative values of suppression/increase (antibunching and bunching) of the density fluctuations at small distances in ideal quantum gases in qualitative agreement with the experimental observation for almost non‐trapped dilute gases.