The upper limit of magnetic field strength in dense stellar hadronic matter

It is shown that in strongly magnetized neutron stars, there exist upper limits of magnetic field strength, beyond which the self energies for both neutron and proton components of neutron star matter become complex in nature. As a consequence they decay within the strong interaction time scale. However, in the ultra-strong magnetic field case, when the zeroth Landau level is only occupied by protons, the system again becomes stable against strong decay.