Relativistic modification of the Gamow factor - art. no. 044905

In processes involving Coulomb-type initial- and final-state interactions, the Gamow factor has been traditionally used to take into account these add itional interactions. The Gamow factor needs to be modified when the magnit ude of the effective coupling constant increases or when the velocity incre ases. For the production of a pair of particles under their mutual Coulomb- type interaction, we obtain the modification of the Gamow factor in terms o f the overlap of the Feynman amplitude with the relativistic wave function of the two particles. As a first example, we study the modification of the Gamow factor for the production of two bosons. The modification is substant ial when the coupling constant is large.