The Lifshitz-Kosevich-Shoenberg theory of relativistic electronic gas in neutron stars

Similar to the de Haas-van Alphen magnetic oscillatory in some normal metals when the Landau quantization is predominant, the magnetic oscillation can also occur in highly degenerate and relativistic electron gas in neutron stars. At large Landau quantum number (Landau quantum number r≥2), we generalize the Lifshitz-Kosevich-Shoenberg theory in non-relativistic electron gas to relativistic gas. At small Landau quantum number (r<2), we expand the grand potential into Fourier series and get similar harmonic oscillatory formula of magnetization. These results indicate that magnetic phase transition similar as Condon transition observed in metals can appear in neutron stars when the differential susceptibility exceeds 1/4π.