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