On The Problem with Only Zeroth Landau Level Occupancy of Electrons / Protons in Strongly Magnetized Neutron Star Matter in $\beta$-equilibrium Condition- The Role of Anomalous Magnetic Moments

It is shown explicitly that if only the zeroth Landau level is occupied by electrons in strongly magnetized neutron star matter in $\beta$-equilibrium condition, then both the proton and neutron matter sectors become spin symmetric. Whereas, the study of Pauli para-magnetism of neutron matter sector shows that such a scenario is physically impossible. It is also shown that in dense stellar hadronic matter in $\beta$-equilibrium in presence of strong quantizing magnetic field, with $\sigma -\omega -\rho$ exchange type mean field interaction and with the inclusion of magnetic dipole moments does not allow electrons to occupy only the zeroth Landau level.