Isothermal compressibility and effects of multibody molecular interactions in a strongly interacting ultracold Fermi gas

We theoretically investigate the isothermal compressibility $\kappa_{T}$ in normal state of an ultracold Fermi gas. Including pairing fluctuations, as well preformed-pair formations, within framework self-consistent $T$-matrix approximation (SCTMA), we evaluate temperature dependence this thermodynamic quantity over entire BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover region. While $\kappa_T$ weak-coupling regime is dominated by atoms near surface, correlations between tightly bound Cooper-pair molecules are found to play crucial roles strong-coupling BEC regime. In latter region, besides a two-body molecular interaction, three-body one shown sizably affect superfluid phase transition temperature. Our results indicate that gas would provide unique opportunity study multi-body molecules.