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 $ρ_c$ and the condensate fraction $ρ_c/ρ$ in terms of the scaled pairing energy gap $Δ/ε_F$, where $ε_F$ is the Fermi energy. We calculate the condensate fraction $ρ_c/ρ$ as a function of the density $ρ$ by using previously obtained results for the pairing gap $Δ$. We find the maximum condensate fraction $(ρ_c/ρ)_{max}= 0.42$ at the density $ρ=5.3\cdot 10^{-4}$ fm$^{-3}$, which corresponds to the Fermi wave number $k_F= 0.25$ fm$^{-1}$.

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