  In the production or annihilation of a pair of fermions, the initial-state or
final-state interactions often lead to significant effects on the reaction
cross sections. For Coulomb-type interactions, the Gamow factor has been
traditionally used to take into account these effects. However the Gamow factor
needs to be modified when the magnitude of the coupling constant or the
relative velocity of two particles increases. We obtain the relativistic
generalization of the Gamow factor in terms of the overlap of the Feynman
amplitude with the relativistic wave function of two fermions with an
attractive Coulomb-type interaction. An explicit form of the corrective factor
is presented for the spin-singlet S-wave state. While the corrective factor
approaches the Gamow factor in the non-relativistic limit, we found that the
Gamow factor significantly over-estimates the effects when the coupling
constant or the velocity is large.
