dorsal/arxiv
View SchemaRelativistic Generalization of the Gamow Factor for Fermion Pair Production or Annihilation
| Authors | Jin-Hee Yoon, Cheuk-Yin Wong |
|---|---|
| Categories | |
| ArXiv ID | nucl-th/0412019 |
| URL | https://arxiv.org/abs/nucl-th/0412019 |
| DOI | 10.1088/0954-3899/31/2/007 |
| Journal | J.Phys. G31 (2005) 149 |
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.
{
"annotation_id": "8c5107b9-7b74-4427-a330-9c387a4e963f",
"date_created": "2026-03-02T18:00:05.031000Z",
"date_modified": "2026-03-02T18:00:05.031000Z",
"file_hash": "cdb3be9ed18ea7a39898d7516ac34501a9a22ca2a2aacfb28366b652144fc6dd",
"private": false,
"record": {
"abstract": "In the production or annihilation of a pair of fermions, the initial-state or\nfinal-state interactions often lead to significant effects on the reaction\ncross sections. For Coulomb-type interactions, the Gamow factor has been\ntraditionally used to take into account these effects. However the Gamow factor\nneeds to be modified when the magnitude of the coupling constant or the\nrelative velocity of two particles increases. We obtain the relativistic\ngeneralization of the Gamow factor in terms of the overlap of the Feynman\namplitude with the relativistic wave function of two fermions with an\nattractive Coulomb-type interaction. An explicit form of the corrective factor\nis presented for the spin-singlet S-wave state. While the corrective factor\napproaches the Gamow factor in the non-relativistic limit, we found that the\nGamow factor significantly over-estimates the effects when the coupling\nconstant or the velocity is large.",
"arxiv_id": "nucl-th/0412019",
"authors": [
"Jin-Hee Yoon",
"Cheuk-Yin Wong"
],
"categories": [
"nucl-th",
"hep-ph"
],
"doi": "10.1088/0954-3899/31/2/007",
"journal_ref": "J.Phys. G31 (2005) 149",
"title": "Relativistic Generalization of the Gamow Factor for Fermion Pair Production or Annihilation",
"url": "https://arxiv.org/abs/nucl-th/0412019"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "a2ecab97-0a24-4977-8908-6e9e4ed8aeff",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}