  Based on the theory of relativistic superstrong magnetic fields(SMFs), by
using the method of the Thomas-Fermi-Dirac approximations, we investigate the
problem of strong electron screening(SES) in SMFs, and the influence of SES on
the nuclear reaction of $^{23}$Mg $(p, \gamma)$$^{24}$Al. Our calculations show
that the nuclear reaction will be markedly effected by the SES in SMFs in the
surface of magnetars. Our calculated screening rates can increase two orders of
magnitude due to SES in SMFs.
