Relativistic Electrons in Super-Strong Magnetic Fields

Based on our previous work we derive a general formula for the pressure of degenerated relativistic-electron gas, P_e.The formula is suitable for electron gas in super-strong magnetic fields.Subsequently, we discuss the Landau levels of electrons and investigate the Quantum Electrodynamic (QED) effects on the equations of states (EOSs) for an n-p-e ideal-gas system, the pressure of which is dominantly from neutrons.Our main conclusions are as follows.(1) The P_e is related to the magnetic induction intensity B, matter density ρ, and electron fraction Y_e.(2) The stronger the magnetic field, the higher the electron pressure.(3) A high electron pressure could be caused by a high Fermi energy of electrons in a super-strong magnetic field.(4) A magnetar could be a neutron star deformed by its anisotropic inner pressure to be near an oblate spheroid and to be more compact than a usual radio pulsar.(5) Because of the positive contribution from the magnetic-field energy a magnetar can have a maximum mass larger than that of a usual radio pulsar.