BEC-BCS crossover and the liquid-gas phase transition in hot and dense nuclear matter

11 pages, 12 figures; v2: minor modifications of the text, references addedThe effect of nucleon-nucleon correlations in symmetric nuclear matter at finite temperature is studied beyond BCS theory. Starting from a Hartree-Fock description of nuclear matter with the Gogny effective interaction, we add correlations corresponding to the formation of preformed pairs and scattering states above the superfluid critical temperature within the in-medium T-matrix approach, which is analogous to the Nozieres-Schmitt-Rink theory. We calculate the critical temperature for a BEC superfluid of deuterons, of a BCS superfluid of nucleons, and in the crossover between these limits. The effect of the correlations on thermodynamic properties (equation of state, energy, entropy) and the liquid-gas phase transition is discussed. Our results show that nucleon-nucleon correlations beyond BCS play an important role for the properties of nuclear matter, especially in the low-density region