Abstract
Formalisms for both non-relativistic and relativistic versions of field emission of electrons in the presence of a strong quantizing magnetic field, relevant for strongly magnetized neutron stars or magnetars, are developed. In the non-relativistic scenario, where electrons obey the Schrodinger equation, we have noticed that when Landau levels are populated for electrons in the presence of a strong quantizing magnetic field the transmission probability exactly vanishes unless the electrons are spin-polarized in the opposite direction to the external magnetic field. On the other hand, cold electron emission under the influence of a strong electrostatic field at the poles is totally forbidden from the surfaces of those compact objects for which the surface magnetic field strength is ≫1015 G (in the eventuality that they may exist). Whereas in the relativistic case electrons obey the Dirac equation, the presence of a strong quantizing magnetic field completely forbids the emission of electrons from the surfaces of compact objects if B > 1013 G.
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