Relativistic Generalization of the Gamow Factor for Fermion Pair Production or Annihilation

Abstract

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.

16 pages, 4 figures in LaTex

References in corpus (8)

• Angular Distributions of Massive Quarks and Leptons Close to Threshold
• Physics of Coulomb Corrections in Hanbury-Brown Twiss Interferometry in Ultrarelativistic Heavy Ion Collisions
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Cited by in corpus (1)

• On relativization of the Sommerfeld-Gamow-Sakharov factor