Abstract
It has been suggested that, in the chiral model of nucleons and pions, the neutral pions form a spatially non-uniform condensate and the spins of nucleons are polarized; therefore, the matter is magnetized at high density. Because of the magnetic moment and/or electric charge, the motion of a proton is controlled by the magnetic field, which is generated by the motion and magnetic moments of other nucleons. We re-examine this phenomenon in a neutron–proton–electron–muon system by taking the magnetic field into account in a self-consistent way. The vacuum values for the magnetic moments are assumed. We find that the protons do not occupy the Landau level with the lowest principal quantum number. The magnetic flux density in matter is of the order of 1015 G, whose effect on the equation of state is very small compared with the pion condensation. The equation of state is softened further as compared to the case in which a pion condensate is absent.
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