Condensate Fraction in Neutron Matter

TL;DR

This paper investigates the Bose-Einstein condensation of fermionic pairs in neutron matter, deriving formulas for the condensate density and fraction, and calculating their dependence on density with a maximum condensate fraction of 0.42.

Contribution

It provides explicit formulas for the condensate density and fraction in neutron matter based on the pairing energy gap, and computes their behavior across different densities.

Findings

Maximum condensate fraction of 0.42 at specific density

Derived explicit formulas relating condensate properties to pairing gap

Calculated condensate fraction as a function of neutron matter density

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 $\Delta/\epsilon_F$, 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$^{-1}$.