BCS-BEC crossover in cold atomic and in nuclear systems

We review the BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover phenomenon discussed in an ultracold Fermi atomic gas and a neutron superfluid in the low-density crust regime of a neutron star. A purpose of this paper is to show that these two very different atomic and nuclear systems can be closely related to each other from the viewpoint of this quantum many-body phenomenon. We explain how the BCS-BEC crossover is realized in the former atomic system by using the novel pairing mechanism called Feshbach resonance. We present a simple explanation for this crossover phenomenon to grasp the essence, as well as detailed microscopic theories that can cover the entire BCS-BEC crossover region. In the latter, we point out that the ordinary BCS theory already has the ability to describe the BCS-BEC crossover at T = 0. At finite temperatures T > 0, however, we need to go beyond this mean-field theory. Besides general aspects of the BCS-BEC crossover phenomenon, we also pick up special topics peculiar to each atomic gas and neutron fluid. The first one is the pseudogap phenomenon in the normal state of a Fermi atomic gas. The second one is the problem of non-zero effective range in an -wave neutron superfluid. (C) 2019 Elsevier B.V. All rights reserved.