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Using the Hellmann--Feynman theorem we analyze the contribution of the different terms of the nucleon-nucleon interaction to the spin symmetry energy of neutron matter. The analysis is performed within the microscopic Brueckner--Hartree--Fock approach using the Argonne V18 realistic potential plus the Urbana IX three-body force. The main contribution to the spin-symmetry energy of neutron matter comes from the S=0 channel, acting only in the non-polarized neutron matter, in particular the $^1S_0$ and the $^1D_2$ partial waves. The importance of correlations in spin-polarized neutron matter is estimated by evaluating the kinetic energy difference between the correlated system and the underlying Fermi sea.
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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.
The equations of state of spin-polarized nuclear matter and pure neutron matter are studied in the framework of the Brueckner-Hartree-Fock theory including a three-body force. The energy per nucleon $E_A(delta)$ calculated in the full range of spin polarization ${delta} = frac{rho_{uparrow}-rho_{downarrow}}{rho}$ for symmetric nuclear matter and pure neutron matter fulfills a parabolic law. In both cases the spin-symmetry energy is calculated as a function of the baryonic density along with the related quantities such as the magnetic susceptibility and the Landau parameter $G_0$. The main effect of the three-body force is to strongly reduce the degenerate Fermi gas magnetic susceptibility even more than the value with only two body force. The EOS is monotonically increasing with the density for all spin-aligned configurations studied here so that no any signature is found for a spontaneous transition to a ferromagnetic state.
The only way neutron matter can couple to the electromagnetic field is through an anomalous coupling, which plays an important role in the thermodynamics of pure neutron matter. Such theories are, however, perturbatively non-renormalisable, which presents a difficulty in terms of the unambiguous treatment of the divergencies. Here we show that despite this, an unambiguous expression can be obtained for the vacuum energy contribution to the grand canonical potential in the case of a constant magnetic field. We find that this contribution is quite small, which justifies the no-sea approximation usually made. We also discuss the density and temperature dependence of the full grand canonical potential.
We analyze the spinodal instabilities of spin polarized asymmetric nuclear matter at zero temperature for several configurations of the neutron and proton spins. The calculations are performed with the Brueckner--Hartree--Fock (BHF) approach using the Argonne V18 nucleon-nucleon potential plus a three-nucleon force of Urbana type. An analytical parametrization of the energy density, which reproduces with good accuracy the BHF results, is employed to determine the spinodal instability region. We find that, independently of the of the orientation of the neutron and proton spins, the spinodal instability region shinks when the system is polarized, being its size smaller smaller when neutron and proton spins are antiparallel than when they are oriented in a parallel way. We find also that the spinodal instability is always dominated by total density fluctuation independently of the degree of polarization of the system, and that restoration of the isospin symmetry in the liquid phase, {it i.e.,} the so-called isospin distillation or fragmentation effect, becomes less efficient with the polarization of the system.
The interior of a neutron star is expected to be occupied by a neutron $^3P_2$ superfluid, which is the condensate of spin-triplet $p$-wave Cooper pairs of neutrons with total angular momentum $J=2$. Here we investigate the thermodynamic stability of $^3P_2$ superfluids in a neutron-star interior under a strong magnetic field. Using the theory incorporating the finite size correction of neutron Fermi surface, we show that the spin-polarized phases of $^3P_2$ superfluids, the magnetized biaxial nematic phase and the ferromagnetic phase, appear in high temperatures and high magnetic fields. These phases were missed in the previous studies using the quasiclassical approximation in which dispersions of neutrons are linearized around the Fermi surface. In particular, the ferromagnetic phase, which is the condensation of Cooper-paired neutrons with fully polarized spins, appears between the normal phase and the biaxial nematic phase and enlarge the thermodynamic stability of $^3P_2$ superfluids under strong magnetic fields. Furthermore, we present the augmented Ginzburg-Landau theory that incorporates the thermodynamic stability of spin-polarized $^3P_2$ superfluid phases.
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