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

Strong screening effects on resonant nuclear reaction $^{23}$Mg $(p,\gamma)$ $^{24}$Al in the surface of magnetars