射电天文研究室知识库

Magnetars are highly-magnetized neutron stars powered by magnetic field energy. Their internal magnetic fields are far higher than the quantum critical magnetic field of electrons. The issue concerning the Landau-level stability of charged particles in a high magnetic field is indeed too complicated, and there has been not any relevant works or explicit analytical expression in the physics community. In this work, we introduce a new quantity, g(n), the Landau-level stability coefficient of electrons in a superstrong magnetic field for illustration of our idea. Considering the uncertainty of the microscopic states of electrons in a superstrong magnetic field, we assume that g(n) takes the form of power exponent, g(n) = g(0)n(alpha); (n >= 1) where n, g(0) and alpha are the Landau level number, the ground-state level stability coefficient, and the stability index of Landau levels of electrons, respectively. It is obvious that gn is the function of n and alpha. When n = 1, g(1) = g(0) i.e., the ground state level has the same stability as that of the first excited level. According to quantum mechanics, the electrons at a higher energy level are prone to have excited transitions towards a lower energy level. The bigger the Landau level number, the shorter the level-occupying time for electrons, and the lower the Landau-level stability, the higher the probability of the excited transition. Since the ground state level has the highest stability and g(n) decreases with the increase in n, the stability index alpha should be negative. The main reasons are as follows: if alpha = 0, then g(n) = g(0)n(alpha) = (n >= 1) = g(0), i.e., all the Landau levels have the same stability, and the maximum of the Landau level number n(max) can take any high value, this scenario is essentially corresponding to a weak magnetic field approximation, which goes against the topic of this paper; if alpha > 0, then a higher Landau-level number possesses a higher stability, and nmax can also take any high value, which is clearly contrary to the principle of quantum mechanics. Based on the analysis above, we conclude that for degenerate and relativistic electrons in a superstrong magnetic field, the Landau-level stability index alpha < 0, and the level stability coefficient gn increases with the increase in alpha for a given Landau level with n >= 1. The bigger the Landau level number n, the faster the change of g(n) with the variation of alpha, and the greater the influence of the stability index alpha on gn, and the larger the probability of a particle's transition (this transition is referred to as the transition from the higher energy level into lower energy level) becomes. By introducing the Dirac-delta function, we deduce a general formula for Fermi energy of degenerate and relativistic electrons, modify a special solution to E-F (e), which is suitable for superstrong magnetic fields, and obtain the magnetic field index beta = 1/6 in the expression of the special solution to E-F (e). The applicable conditions for the special solution to E-F (e), as well as its general expression, are constrained as rho >= 10(7) g.cm(3) and B-cr << B << 10(17) G.