Physics – Nuclear Physics – Nuclear Theory
Scientific paper
2004-12-06
J.Phys. G31 (2005) 149
Physics
Nuclear Physics
Nuclear Theory
16 pages, 4 figures in LaTex
Scientific paper
10.1088/0954-3899/31/2/007
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.
Wong Cheuk-Yin
Yoon Jin-Hee
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