Condensate Fraction in Neutron Matter

Abstract

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 $\Delta /{ϵ}_F$, where ${ϵ}_F$ 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${}^{-1}$.

Comments: 4 pages, 3 figures, to be published in Phys. Rev. C