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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.
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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$^{-1}$.
We present variational Monte Carlo calculations of the neutron matter equation of state using chiral nuclear forces. The ground-state wavefunction of neutron matter, containing non-perturbative many-body correlations, is obtained from auxiliary-field quantum Monte Carlo simulations of up to about 340 neutrons interacting on a 10^3 discretized lattice. The evolution Hamiltonian is chosen to be attractive and spin-independent in order to avoid the fermion sign problem and is constructed to best reproduce broad features of the chiral nuclear force. This is facilitated by choosing a lattice spacing of 1.5 fm, corresponding to a momentum-space cutoff of Lambda = 414 MeV/c, a resolution scale at which strongly repulsive features of nuclear two-body forces are suppressed. Differences between the evolution potential and the full chiral nuclear interaction (Entem and Machleidt Lambda = 414 MeV) are then treated perturbatively. Our results for the equation of state are compared to previous quantum Monte Carlo simulations which employed chiral two-body forces at next-to-next-to-leading order (N2LO). In addition we include the effects of three-body forces at N2LO, which provide important repulsion at densities higher than 0.02 fm^-3, as well as two-body forces at N3LO.
Based on an equivparticle model, we investigate the in-medium quark condensate in neutron stars. Carrying out a Taylor expansion of the nuclear binding energy to the order of $rho^3$, we obtain a series of EOSs for neutron star matter, which are confronted with the latest nuclear and astrophysical constraints. The in-medium quark condensate is then extracted from the constrained properties of neutron star matter, which decreases non-linearly with density. However, the chiral symmetry is only partially restored with non-vanishing quark condensates, which may vanish at a density that is out of reach for neutron stars.
We show that microscopic calculations based on chiral effective field theory interactions constrain the properties of neutron-rich matter below nuclear densities to a much higher degree than is reflected in commonly used equations of state. Combined with observed neutron star masses, our results lead to a radius R = 9.7 - 13.9 km for a 1.4 M_{solar} star, where the theoretical range is due, in about equal amounts, to uncertainties in many-body forces and to the extrapolation to high densities.
We study the possible collective plasma modes which can affect neutron-star thermodynamics and different elementary processes in the baryonic density range between nuclear saturation ($rho_0$) and $3rho_0$. In this region, the expected constituents of neutron-star matter are mainly neutrons, protons, electrons and muons ($npemu$ matter), under the constraint of beta equilibrium. The elementary plasma excitations of the $pemu$ three-fluid medium are studied in the RPA framework. We emphasize the relevance of the Coulomb interaction among the three species, in particular the interplay of the electron and muon screening in suppressing the possible proton plasma mode, which is converted into a sound-like mode. The Coulomb interaction alone is able to produce a variety of excitation branches and the full spectral function shows a rich structure at different energy. The genuine plasmon mode is pushed at high energy and it contains mainly an electron component with a substantial muon component, which increases with density. The plasmon is undamped for not too large momentum and is expected to be hardly affected by the nuclear interaction. All the other branches, which fall below the plasmon, are damped or over-damped.
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