BCS-BEC crossover of neutron pairs in symmetric and asymmetric nuclear matter

We propose new types of density-dependent contact pairing interactions which reproduce the pairing gaps in symmetric and neutron matters obtained by a microscopic treatment based on realistic nucleon nucleon interaction. These interactions are able to simulate the pairing gaps of either the bare interaction or the interaction screened by the medium polarization effects. It is shown that the medium polarization effects cannot be cast into the usual density power law function of the contact interaction and require the introduction of another isoscalar term. The BCS-BEC crossover of neutron pairs in symmetric and asymmetric nuclear matters is studied by using these contact interactions. This work shows that the bare and screened pairing interactions lead to different features of the BCS-BEC crossover in symmetric nuclear matter. For the screened pairing interaction, a two-neutron BEC state is formed in symmetric matter at k_Fn~0.2 fm^-1 (neutron density ρ_n/ρ₀~10^-3). In contrast, the bare interaction does not form the BEC state at any neutron density.