Condensate fraction in neutron matter

We study the Bose-Einstein condensation of fermionic pairs in the uniform neutron matter by using the concept of the off-diagonal long-range order of the two-body density matrix of the system. We derive explicit formulas for the condensate density ρcon and the condensate fraction ρcon/ρ in terms of the scaled pairing energy gap Δ/εF where εF is the Fermi energy. We calculate the condensate fraction ρcon/ρ as a function of the density ρ by using previously obtained results for the pairing gap Δ. We find the maximum condensate fraction (ρcon/ρ)max=0.42 at the density ρ=5.3×10−4 fm−3, which corresponds to the Fermi wave number kF=0.25 fm−1.