Brief ReviewNo Access

TECHNIQUES IN ANALYTIC LAMB SHIFT CALCULATIONS

ULRICH D. JENTSCHURA

Max-Planck-Institut für Kernphysik, Saupfercheckweg 1, 69117 Heidelberg, Germany

https://doi.org/10.1142/S0217732305018256Cited by:4 (Source: Crossref)

Abstract

Quantum electrodynamics has been the first theory to emerge from the ideas of regularization and renormalization, and the coupling of the fermions to the virtual excitations of the electromagnetic field. Today, bound-state quantum electrodynamics provides us with accurate theoretical predictions for the transition energies relevant to simple atomic systems, and steady theoretical progress relies on advances in calculational techniques, as well as numerical algorithms. In this brief review, we discuss one particular aspect connected with the recent progress: the evaluation of relativistic corrections to the one-loop bound-state self-energy in a hydrogenlike ion of low nuclear charge number, for excited non-S states, up to the order of α(Zα)⁶ in units of the electron mass. A few details of calculations formerly reported in the literature are discussed, and results for 6F, 7F, 6G and 7G states are given.

Keywords:

PACS: 31.30.Jv, 12.20.Ds, 11.10.St

References

R. P. Feynman, Phys. Rev. 74, 1430 (1948). Crossref, Web of Science, ADS, Google Scholar
N. M. Kroll and W. E. Lamb, Phys. Rev. 75, 388 (1949). Crossref, Web of Science, ADS, Google Scholar
J. B. French and V. F. Weisskopf, Phys. Rev. 75, 1240 (1949). Crossref, Web of Science, ADS, Google Scholar
R. P. Feynman, Phys. Rev. 76, 769 (1949). Crossref, Web of Science, ADS, Google Scholar
V. B. Berestetskii , E. M. Lifshitz and L. P. Pitaevskii , Quantum Electrodynamics ( Pergamon Press , 1982 ) . Google Scholar
W. E. Caswell and G. P. Lepage, Phys. Lett. B167, 437 (1986). ADS, Google Scholar
T. Kinoshita and M. Nio, Phys. Rev. D53, 4909 (1996). ADS, Google Scholar
M. Nio and T. Kinoshita, Phys. Rev. D55, 7267 (1997). ADS, Google Scholar
A. Pineda and J. Soto, Phys. Rev. D59, 016005 (1998). Google Scholar
M. Nieringet al., Phys. Rev. Lett. 84, 5496 (2000). Crossref, Web of Science, ADS, Google Scholar
T. Udemet al., Phys. Rev. Lett. 79, 2646 (1997). Crossref, Web of Science, ADS, Google Scholar
B. de Beauvoiret al., Phys. Rev. Lett. 78, 440 (1997). Crossref, Web of Science, ADS, Google Scholar
U. Jentschura and K. Pachucki, Phys. Rev. A54, 1853 (1996). Google Scholar
U. D. Jentschuraet al., Phys. Rev. Lett. (2005). Google Scholar
P. J. Mohr and B. N. Taylor, Rev. Mod. Phys. 77, 1 (2005). Crossref, Web of Science, ADS, Google Scholar
A. Poquerusse, Phys. Lett. A82, 232 (1981). ADS, Google Scholar
U. D. Jentschura, J. Phys. A36, L229 (2003). Google Scholar
U. D. Jentschuraet al., Phys. Rev. Lett. 90, 163001 (2003). Crossref, Web of Science, ADS, Google Scholar
S. Wolfram , Mathematica-A System for Doing Mathematics by Computer ( Addison-Wesley , 1988 ) . Google Scholar
E.-O. Le Bigotet al., Phys. Rev. A68, 042101 (2003). Google Scholar
K. Pachucki, Ann. Phys. (N. Y.) 226, 1 (1993). Crossref, Web of Science, ADS, Google Scholar
U. D. Jentschura, Theory of the Lamb Shift in Hydrogenlike Systems, hep-ph/0305065; based on an unpublished "Master Thesis: The Lamb Shift in Hydrogenlike Systems", (in German: "Theorie der Lamb–Verschiebung in wasserstoffartigen Systemen"), Ludwig-Maximilians-University of Munich, Germany (1996) . Google Scholar
C. Itzykson and J. B. Zuber , Quantum Field Theory ( McGraw-Hill , 1980 ) . Google Scholar
U. D. Jentschura and K. Pachucki, J. Phys. A35, 1927 (2002). Google Scholar
U. D. Jentschura, C. H. Keitel and K. Pachucki, Can. J. Phys. 80, 1213 (2002). Crossref, Web of Science, ADS, Google Scholar
U. D. Jentschuraet al., New J. Phys. 4, 49 (2002). Crossref, Web of Science, Google Scholar
K. Pachucki, Phys. Rev. A69, 052502 (2004). Google Scholar
U. D. Jentschura, G. Soff and P. J. Mohr, Phys. Rev. A56, 1739 (1997). ADS, Google Scholar
R. A. Swainson and G. W. F. Drake, J. Phys. A24, 79 (1991). ADS, Google Scholar
R. A. Swainson and G. W. F. Drake, J. Phys. A24, 95 (1991). ADS, Google Scholar
R. A. Swainson and G. W. F. Drake, J. Phys. A24, 1801 (1991). Google Scholar
S. Salomonson and P. Öster, Phys. Rev. A40, 5559 (1989). ADS, Google Scholar
K. Pachucki and U. D. Jentschura, Phys. Rev. Lett. 91, 113005 (2003). Crossref, Web of Science, ADS, Google Scholar
U. D. Jentschura, Phys. Rev. A70, 052108 (2004). Google Scholar
K. Pachucki, J. Phys. B32, 137 (1999). ADS, Google Scholar
A. Pineda, Phys. Rev. A66, 062108 (2002). Google Scholar
A. Pineda, Phys. Rev. D66, 054022 (2002). Google Scholar
J. Sapirstein and D. R. Yennie, Quantum Electrodynamics, Advanced Series on Directions in High Energy Physics 7, ed. T. Kinoshita (World Scientific, 1990) pp. 560–672. Link, Google Scholar
P. J. Mohr and B. N. Taylor, Rev. Mod. Phys. 72, 351 (2000). Crossref, Web of Science, ADS, Google Scholar
H. A. Bethe, Phys. Rev. 72, 339 (1947). Crossref, Web of Science, ADS, Google Scholar
U. D. Jentschura, P. J. Mohr and G. Soff, Phys. Rev. Lett. 82, 53 (1999). Crossref, Web of Science, ADS, Google Scholar
U. D. Jentschura, P. J. Mohr and G. Soff, Phys. Rev. A63, 042512 (2001). Google Scholar
U. D. Jentschura and P. J. Mohr, Phys. Rev. A69, 064103 (2004). Google Scholar
U. D. Jentschuraet al., Comput. Phys. Commun. 116, 28 (1999). Crossref, Web of Science, ADS, Google Scholar
S. V. Aksenovet al., Comput. Phys. Commun. 150, 1 (2003). Crossref, Web of Science, ADS, Google Scholar