Late-time evolution of charged massive Dirac fields in the Reissner-Nordstr\"om black-hole background

The late-time evolution of the charged massive Dirac fields in the background of a Reissner-Norstr\"om (RN) black hole is studied. It is found that the intermediate late-time behavior is dominated by an inverse power-law decaying tail without any oscillation in which the dumping exponent depends not only on the multiple number of the wave mode but also on the field parameters. It is also found that, at very late times, the oscillatory tail has the decay rate of $t^{-5/6}$ and the oscillation of the tail has the period $2\pi/\mu$ which is modulated by two types of long-term phase shifts.