The Physics of Magnetars II - The Electron Fermi Energy of and the   Origin of High X-ray Luminosity of Magnetars
  In this paper we discuss in detail the quantization of Landau energy levels of a strongly magnetized and completely degenerate relativistic electron gas in neutron stars. In particular, we focus on the Fermi energy dependence of the magnetic field for a relativistic electron gas in the superstrong magnetic field of magnetars. We would like to point out that some of the results concerning the microscopic number density of states of a strongly magnetized electron gas given by well-known statistical physics text books are incorrect. The repeated use of these results in the last five decades probably seriously affects the physics of neutron stars and magnetars. The quantization of Landau energy levels is accurately delineated in terms of the Dirac (delta) function. Relatively simple calculation shows that the Fermi energy of relativistic electron gas in magnetars with superstrong magnetic fields( B > Bcr , here Bcr is the Landau critical magnetic field) increases with magnetic fieldstrength as B**(1/4). On the basis of this simple but importantnew result we are leading naturally to propose a new mechanism for the production of high X-ray luminosity from magnetars. 
Qiu-he Peng, Jie Zhang, Chih-kang Chou and Zhi-fu Gao
astro-ph.HE