dorsal/arxiv
View SchemaSelf-Energy Correction to the Two-Photon Decay Width in Hydrogenlike Atoms
| Authors | U. D. Jentschura |
|---|---|
| Categories | |
| ArXiv ID | physics/0410057 |
| URL | https://arxiv.org/abs/physics/0410057 |
| DOI | 10.1103/PhysRevA.69.052118 |
| Journal | Phys.Rev. A69 (2004) 052118 |
Abstract
We investigate the gauge invariance of the leading logarithmic radiative correction to the two-photon decay width in hydrogenlike atoms. It is shown that an effective treatment of the correction using a Lamb-shift "potential" leads to equivalent results in both the length as well as the velocity gauges provided all relevant correction terms are taken into account. Specifically, the relevant radiative corrections are related to the energies that enter into the propagator denominators, to the Hamiltonian, to the wave functions, and to the energy conservation condition that holds between the two photons; the form of all of these effects is different in the two gauges, but the final result is shown to be gauge invariant, as it should be. Although the actual calculation only involves integrations over nonrelativistic hydrogenic Green functions, the derivation of the leading logarithmic correction can be regarded as slightly more complex than that of other typical logarithmic terms. The dominant radiative correction to the 2S two-photon decay width is found to be -2.020536 (alpha/pi) (Zalpha)^2 ln[(Zalpha)^-2] in units of the leading nonrelativistic expression. This result is in agreement with a length-gauge calculation [S. G. Karshenboim and V. G. Ivanov, e-print physics/9702027], where the coefficient was given as -2.025(1).
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"abstract": "We investigate the gauge invariance of the leading logarithmic radiative\ncorrection to the two-photon decay width in hydrogenlike atoms. It is shown\nthat an effective treatment of the correction using a Lamb-shift \"potential\"\nleads to equivalent results in both the length as well as the velocity gauges\nprovided all relevant correction terms are taken into account. Specifically,\nthe relevant radiative corrections are related to the energies that enter into\nthe propagator denominators, to the Hamiltonian, to the wave functions, and to\nthe energy conservation condition that holds between the two photons; the form\nof all of these effects is different in the two gauges, but the final result is\nshown to be gauge invariant, as it should be. Although the actual calculation\nonly involves integrations over nonrelativistic hydrogenic Green functions, the\nderivation of the leading logarithmic correction can be regarded as slightly\nmore complex than that of other typical logarithmic terms. The dominant\nradiative correction to the 2S two-photon decay width is found to be -2.020536\n(alpha/pi) (Zalpha)^2 ln[(Zalpha)^-2] in units of the leading nonrelativistic\nexpression. This result is in agreement with a length-gauge calculation [S. G.\nKarshenboim and V. G. Ivanov, e-print physics/9702027], where the coefficient\nwas given as -2.025(1).",
"arxiv_id": "physics/0410057",
"authors": [
"U. D. Jentschura"
],
"categories": [
"physics.atom-ph"
],
"doi": "10.1103/PhysRevA.69.052118",
"journal_ref": "Phys.Rev. A69 (2004) 052118",
"title": "Self-Energy Correction to the Two-Photon Decay Width in Hydrogenlike Atoms",
"url": "https://arxiv.org/abs/physics/0410057"
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