Neutron matter under strong magnetic fields: A comparison of models

The equation of state of neutron matter is affected by the presence of a magnetic field due to the intrinsic magnetic moment of the neutron. Here we study the equilibrium configuration of this system for a wide range of densities, temperatures, and magnetic fields. Special attention is paid to the behavior of the isothermal compressibility and the magnetic susceptibility. Our calculation is performed using both microscopic and phenomenological approaches of the neutron matter equation of state, namely the Brueckner-Hartree-Fock (BHF) approach using the Argonne V18 nucleon-nucleon potential supplemented with the Urbana IX three-nucleon force, the effective Skyrme model in a Hartree-Fock description, and the quantum hadrodynamic formulation with a mean-field approximation. All these approaches predict a change from completely spin polarized to partially polarized matter that leads to a continuous equation of state. The compressibility and the magnetic susceptibility show characteristic behaviors which reflect that fact. Thermal effects tend to smear out the sharpness found for these quantities at $T=0$. In most cases a thermal increase of $\Delta T=10$ MeV is enough to hide the signals of the change of polarization. The set of densities and magnetic field intensities for which the system changes it spin polarization is different for each model. However, we found that under the conditions examined in this work there is an overall agreement between the three theoretical descriptions.

Figure 1

Spin asymmetry as a function of the density at $B=2.5\times {10}^{18}$ G and $T=0$ (a) and $T=10$ MeV (b) for the three models considered.

Figure 2

Same as Fig. 1 for $B={10}^{19}$ G.

Figure 3

Spin asymmetry as a function of the magnetic field intensity for $n/n_0=0.2$ and $T=0$ (a) and $T=10$ MeV (b) for the three models considered. The magnetic filed intensity is given in units of ${10}^{18}$ G.

Figure 4

(a) Average effective mass as a function of the density at $T=0$ MeV for $B={10}^{19}$G. (b) Average effective mass as a function of the magnetic field intensity for $n/n_0=0.2$ and $T=0$. The magnetic filed intensity is given in units of ${10}^{18}$ G.

Figure 5

Neutron-up and neutron-down effective masses as a function of the density for $T=0$ MeV and $B=2.5\times {10}^{18}$ G (a) and $B={10}^{19}$ G (b). Results are shown only for the BHF and Skyrme models.

Figure 6

Free energy per particle as a function of the density for $T=0$ MeV and $B=2.5\times {10}^{18}$ G (a) and $B={10}^{19}$ G (b).

Figure 7

Pressure as a function of the density for $T=0$ MeV and $B=2.5\times {10}^{18}$ G (a) and $B={10}^{19}$ G (b).

Figure 8

Isothermal compressibility as a function of the density for $T=0$ MeV and $B=2.5\times {10}^{18}$ G (a) and $B={10}^{19}$ G (b).

Figure 9

Same as Fig. 8 for $T=10$ MeV.

Figure 10

Isothermal compressibility as a function of the magnetic field intensity for $n/n_0=0.2$ and $T=0$ MeV (a) and $T=10$ MeV (b). The magnetic field intensity is given in units of ${10}^{18}$ G.

Figure 11

Magnetic susceptibility over ${\kappa }^2$ as a function of the density for $T=0$ MeV and $B=2.5\times {10}^{18}$ G (a) and $B={10}^{19}$ G (b).

Figure 12

Same as Fig. 11 for $T=10$ MeV.

Figure 13

Magnetic susceptibility over ${\kappa }^2$ as a function of the magnetic field intensity for $n/n_0=0.2$ and $T=0$ MeV (a) and $T=10$ MeV (b). The magnetic field intensity is given in units of ${10}^{18}$ G.