Nucleon Instability in a Degenerate Magnetized Nucleon–Electron Gas

In the framework of the model of a degenerate relativistic ideal neutron–proton–electron gas($np^+e^-$-gas) in an external superstrong constant and homogeneous magnetic field, we study the effect of the magnetic field on the state of chemical equilibrium of the $np^+e^-$-gas and on the processes of electronic ($\beta^-$) and positronic ($\beta^+$) nucleon decay taking the effects due to the interaction between the nucleon anomalous magnetic moments and the magnetic field into account. For sufficiently large values of the magnetic induction, the proton density in chemical equilibrium must exceed the neutron density. Including the interaction between the nucleon anomalous magnetic moments $M_{n,p}$ and the magnetic field results in an insignificant reduction of the proton density, but, as in the case $M_{n,p}=0$ the proton density in chemical equilibrium in the presence of the superstrong magnetic field exceeds the neutron density. We show that if the interaction between the nucleon anomalous magnetic moments and the superstrong magnetic field is taken into account, then the positronic decay of a free proton (i.e., a proton not entering the composition of an atomic nucleus) into a neutron, a positron, and a neutrino can become energetically allowed. We discuss the necessary conditions for realizing the phase transition from the nucleon phase to the quark phase of the substance in the central region of a strongly magnetized neutron star.