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Register a new userCondensate Fraction in Neutron Matter
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Authors
Luca Salasnich
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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 $rho=5.3cdot 10^{-4}$ fm$^{-3}$, which corresponds to the Fermi wave number $k_F= 0.25$ fm$^{-1}$.
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We calculate the chiral condensate in neutron matter at zero temperature based on nuclear forces derived within chiral effective field theory. Two-, three- and four-nucleon interactions are included consistently to next-to-next-to-next-to-leading order (N3LO) of the chiral expansion. We find that the interaction contributions lead to a modest increase of the condensate, thus impeding the restoration of chiral symmetry in dense matter and making a chiral phase transition in neutron-rich matter unlikely for densities that are not significantly higher than nuclear saturation density.
We study the properties of a spin-down neutron impurity immersed in a low-density free Fermi gas of spin-up neutrons. In particular, we analyze its energy ($E_downarrow$), effective mass ($m^*_downarrow$) and quasiparticle residue ($Z_downarrow$). Results are compared with those of state-of-the-art quantum Monte Carlo calculations of the attractive Fermi polaron realized in ultracold atomic gases experiments, and with those of previous studies of the neutron polaron. Calculations are performed within the Brueckner--Hartree--Fock approach using the chiral two-body nucleon-nucleon interaction of Entem and Machleidt at N$^3$LO with a 500 MeV cut-off and the Argonne V18 phenomenological potential. Only contributions from the $^1S_0$ partial wave, which is the dominant one in the low-density region considered, are included. Contributions from three-nucleon forces are expected to be irrelevant at these densities and, therefore, are neglected in the calculation. Our results show that for Fermi momenta between $sim 0.25$ and $sim 0.45$ fm$^{-1}$ the energy, effective mass and quasiparticle residue of the impurity vary only slightly, respectively, in the ranges $-0.604,E_F < E_downarrow < -0.635,E_F $, $1.300,m < m^*_downarrow < 1.085, m$ and $0.741 <Z_downarrow< 0.836$ in the case of the chiral interaction, and $-0.621,E_F < E_downarrow < -0.643,E_F $, $1.310,m < m^*_downarrow < 1.089, m$ and $0.739 <Z_downarrow< 0.832$ when using the Argonne V18 potential. These results are compatible with those derived from ultracold atoms and show that a spin-down neutron impurity in a free Fermi gas of spin-up neutrons with a Fermi momentum in the range $0.25lesssim k_F lesssim 0.45$ fm$^{-1}$ exhibits properties very similar to those of an attractive Fermi polaron in the unitary limit.
We review the properties of neutron matter in the low-density regime. In particular, we revise its ground state energy and the superfluid neutron pairing gap, and analyze their evolution from the weak to the strong coupling regime. The calculations of the energy and the pairing gap are performed, respectively, within the Brueckner--Hartree--Fock approach of nuclear matter and the BCS theory using the chiral nucleon-nucleon interaction of Entem and Machleidt at N$^3$LO and the Argonne V18 phenomenological potential. Results for the energy are also shown for a simple Gaussian potential with a strength and range adjusted to reproduce the $^1S_0$ neutron-neutron scattering length and effective range. Our results are compared with those of quantum Monte Carlo calculations for neutron matter and cold atoms. The Tan contact parameter in neutron matter is also calculated finding a reasonable agreement with experimental data with ultra-cold atoms only at very low densities. We find that low-density neutron matter exhibits a behavior close to that of a Fermi gas at the unitary limit, although, this limit is actually never reached. We also review the properties (energy, effective mass and quasiparticle residue) of a spin-down neutron impurity immersed in a low-density free Fermi gas of spin-up neutrons already studied by the author in a recent work where it was shown that these properties are very close to those of an attractive Fermi polaron in the unitary limit.
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