We find that the electron Fermi energy,  , increases with the magnetic field strength and it is proportional to  . We note that this result is exactly the opposite of the popular idea that the electron Fermi energy decreases with the magnetic field. The key reason for the dilemma is that an incorrect formulae of the microscopic number of states for the electrons in intense magnetic field from some internationally well known popular textbooks on statistical physics has been repeatedly quoted by many authors.
3. We propose a new mechanism for the production of the high soft X-ray luminosities of magnetars. In particular, the Fermi energy of the electrons is higher than 60MeV in ultra-strong magnetic fields, B>> Bcr (=4.4141013 gauss), which is much higher than the Fermi energy of the neutrons.