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Title: All-order results for the one-loop QED correction to the hyperfine structure in light H-like atoms

Abstract

A calculation of the one-loop self-energy and vacuum-polarization corrections to the hyperfine splitting of the 1s and 2s states in light H-like ions is carried out to all orders in the parameter Z{alpha}. Using the known values for the Z{alpha}-expansion coefficients, the numerical data obtained are extrapolated from Z=5 and higher to Z=0, 1, and 2, with the resulting accuracy being significantly better than in previous evaluations. Our calculation shifts the theoretical value of the normalized difference of the 1s and 2s hyperfine-structure intervals in {sup 3}He{sup +} by 0.056 kHz and improves its accuracy.

Authors:
 [1];  [2];  [1];  [1];  [3];  [4]
  1. Department of Physics, St. Petersburg State University, Oulianovskaya 1, Petrodvorets, St. Petersburg 198504 (Russian Federation)
  2. (Russian Federation)
  3. (Germany)
  4. Institut fuer Theoretische Physik, TU Dresden, Mommsenstrasse 13, D-01062 Dresden (Germany)
Publication Date:
OSTI Identifier:
20786499
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. A; Journal Volume: 72; Journal Issue: 5; Other Information: DOI: 10.1103/PhysRevA.72.052510; (c) 2005 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
74 ATOMIC AND MOLECULAR PHYSICS; ACCURACY; ATOMS; CATIONS; CORRECTIONS; EVALUATION; EXPANSION; HELIUM IONS; HYPERFINE STRUCTURE; QUANTUM ELECTRODYNAMICS; SELF-ENERGY; VACUUM POLARIZATION

Citation Formats

Yerokhin, V. A., Center for Advanced Studies, St. Petersburg State Polytechnical University, Polytekhnicheskaya 29, St. Petersburg 195251, Artemyev, A. N., Shabaev, V. M., Max-Planck-Institut fuer Physik Komplexer Systeme, Noethnitzer Strasse 38, D-01187 Dresden, and Plunien, G.. All-order results for the one-loop QED correction to the hyperfine structure in light H-like atoms. United States: N. p., 2005. Web. doi:10.1103/PHYSREVA.72.0.
Yerokhin, V. A., Center for Advanced Studies, St. Petersburg State Polytechnical University, Polytekhnicheskaya 29, St. Petersburg 195251, Artemyev, A. N., Shabaev, V. M., Max-Planck-Institut fuer Physik Komplexer Systeme, Noethnitzer Strasse 38, D-01187 Dresden, & Plunien, G.. All-order results for the one-loop QED correction to the hyperfine structure in light H-like atoms. United States. doi:10.1103/PHYSREVA.72.0.
Yerokhin, V. A., Center for Advanced Studies, St. Petersburg State Polytechnical University, Polytekhnicheskaya 29, St. Petersburg 195251, Artemyev, A. N., Shabaev, V. M., Max-Planck-Institut fuer Physik Komplexer Systeme, Noethnitzer Strasse 38, D-01187 Dresden, and Plunien, G.. Tue . "All-order results for the one-loop QED correction to the hyperfine structure in light H-like atoms". United States. doi:10.1103/PHYSREVA.72.0.
@article{osti_20786499,
title = {All-order results for the one-loop QED correction to the hyperfine structure in light H-like atoms},
author = {Yerokhin, V. A. and Center for Advanced Studies, St. Petersburg State Polytechnical University, Polytekhnicheskaya 29, St. Petersburg 195251 and Artemyev, A. N. and Shabaev, V. M. and Max-Planck-Institut fuer Physik Komplexer Systeme, Noethnitzer Strasse 38, D-01187 Dresden and Plunien, G.},
abstractNote = {A calculation of the one-loop self-energy and vacuum-polarization corrections to the hyperfine splitting of the 1s and 2s states in light H-like ions is carried out to all orders in the parameter Z{alpha}. Using the known values for the Z{alpha}-expansion coefficients, the numerical data obtained are extrapolated from Z=5 and higher to Z=0, 1, and 2, with the resulting accuracy being significantly better than in previous evaluations. Our calculation shifts the theoretical value of the normalized difference of the 1s and 2s hyperfine-structure intervals in {sup 3}He{sup +} by 0.056 kHz and improves its accuracy.},
doi = {10.1103/PHYSREVA.72.0},
journal = {Physical Review. A},
number = 5,
volume = 72,
place = {United States},
year = {Tue Nov 15 00:00:00 EST 2005},
month = {Tue Nov 15 00:00:00 EST 2005}
}
  • A lattice action for QED is considered, where the derivatives in the Dirac operator are replaced by one-sided lattice differences. A systematic expansion in the lattice spacing of the one-loop contribution to the fermion self-energy, vacuum polarization tensor, and vertex function is carried out for an arbitrary choice of one-sided lattice differences. It is shown that only the vacuum polarization tensor possesses the correct continuum limit, while the fermion self-energy and vertex function receive noncovariant contributions. A lattice action, discretized with a fixed choice of one-sided lattice differences, therefore, does not define a renormalizable field theory. The noncovariant contributions can,more » however, be eliminated by averaging the expression over all possible choices of one-sided lattice differences. {copyright} {ital 1997} {ital The American Physical Society}« less
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