Impossibility of Spin Polarized States for Neutron Star / Proto-neutron Star Matter in β-Equilibrium Condition

It is shown explicitly that a ferromagnetic transition of neutron star (NS) / proto-neutron star (PNS) matter in the $\beta$-equilibrium condition with $\sigma-\omega-\rho$ exchange type of mean field approximation can actually occur if and only if the neutrinos remain trapped within the system, and perhaps it is also necessary for the neutrinos / anti-neutrinos to carry some finite non-zero mass. It is further shown that the electrons also play a significant role in this transition process. It is therefore, very much unlikely that such a transition of spin polarization can really take place in old neutron stars of very low temperature, whereas, the possibility of spontaneous ferromagnetic transition cannot be ruled out in a newly born PNS.