A model of a degenerate neutron gas in chemical equilibrium with a background of degenerate electrons and protons in a constant uniform ultrastrong magnetic field is applied to describe the state of matter in the cores of strongly magnetized neutron stars. Expressions for the thermodynamic quantities are obtained including the anomalous magnetic moments of the fermions. It is shown that (1) the inclusion of the anomalous magnetic moments of charged fermions leads to nonperiodic magnetic oscillations of their thermodynamic quantities in strong magnetic fields, (2) the total stress energy tensor relevant for neutron star structure must include contributions from both the magnetized matter and the magnetic field and as a result the total pressure produced is anisotropic, and (3) complete spin polarization of neutrons occurring in superstrong magnetic fields must lead to an increase in the degeneracy pressure compared with the zero field case at the same neutron densities. It is hoped that the results obtained will have applications for the structure in neutron stars with ultrastrong frozen-in magnetic fields.
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