Abstract
While taking into account the nuclear-structure contributions to the Lamb shift, one has to make various subtractions for the two-photon exchange contributions. Such subtractions should be consistent with the structureless part of theory. We study here the subtractions for a two-body atomic systems which consist of a pointlike lepton (an electron or a muon) and a nucleus with spin 0, 1/2, and 1, and find the recoil contribution in order (Zα)5 due to the subtractions for I = 0, 1. (The related contribution to the energy levels for I = 1∕2 of order (Zα)5m is called the Salpeter term.)
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References
H. Grotch, D.R. Yennie, Rev. Mod. Phys. 41, 350 (1969)
G.P. Lepage, Phys. Rev. A 16, 863 (1977)
G.T. Bodwin, D.R. Yennie, M.A. Gregorio, Rev. Mod. Phys. 57, 723 (1985)
M.I. Eides, S.G. Karshenboim, V.A. Shelyuto, Ann. Phys. 205, 231 (1991)
W.E. Caswell, G.P. Lepage, Phys. Lett. B 167, 437 (1986)
E.Yu. Korzinin, V.A. Shelyuto, V.G. Ivanov, S.G. Karshenboim, Phys. Rev. A 97, 012514 (2018)
A. Antognini, F. Nez, K. Schuhmann, F.D. Amaro, F. Biraben, J.M.R. Cardoso, D.S. Covita, A. Dax, S. Dhawan, M. Diepold, L.M.P. Fernandes, A. Giesen, A.L. Gouvea, T. Graf, T.W. Hänsch, P. Indelicato, L. Julien, Cheng-Yang Kao, P. Knowles, F. Kottmann, E.-O. Le Bigot, Y.-W. Liu, J.A.M. Lopes, L. Ludhova, C.M.B. Monteiro, F. Mulhauser, T. Nebel, P. Rabinowitz, J.M.F. dos Santos, L.A. Schaller, C. Schwob, D. Taqqu, J.F.C.A. Veloso, J. Vogelsang, R. Pohl, Science 339, 417 (2013)
R. Pohl, F. Nez, L.M.P. Fernandes, F.D. Amaro, F. Biraben, J.M.R. Cardoso, D.S. Covita, A. Dax, S. Dhawan, M. Diepold, A. Giesen, A.L. Gouvea, T Graf, T.W. Hänsch, P. Indelicato, L. Julien, P. Knowles, F. Kottmann, E.-O. Le Bigot, Y.-W. Liu, J.A.M. Lopes, L. Ludhova, C.M.B. Monteiro, F. Mulhauser, T. Nebel, P. Rabinowitz, J.M.F. dos Santos, L.A. Schaller, K. Schuhmann, C. Schwob, D. Taqqu, J.F.C.A. Veloso, A. Antognini, Science 353, 669 (2016)
T. Nebel, F.D. Amaro, A. Antognini, F. Biraben, J.M.R. Cardoso, D.S. Covita, A. Dax, L.M.P. Fernandes, A.L. Gouvea, T. Graf, T.W. Hänsch, M. Hildebrandt, P. Indelicato, L. Julien, K. Kirch, F. Kottmann, Y.-W. Liu, C.M.B. Monteiro, F. Nez, J.M.F. dos Santos, K. Schuhmann, D. Taqqu, J.F.C.A. Veloso, A. Voss, R. Pohl, Hyp. Int. 212, 195 (2012)
R. Arnowitt, Phys. Rev. 92, 1002 (1953)
W.A. Newcomb, E.E. Salpeter, Phys. Rev. 97, 1146 (1955)
E.E. Salpeter, Phys. Rev. 87, 328 (1952)
T. Fulton, P.C. Martin, Phys. Rev. 95, 811 (1954)
H.A. Bethe, E.E. Salpeter, Quantum Mechanics of One and Two Electron Atoms (Springer-Verlag, Berlin, 1957)
G.W. Erickson, J. Phys. Chem. Ref. Data 6, 831 (1977)
J. Sapirstein, D.R. Yennie, in Quantum Electrodynamics, edited by T. Kinoshita (World Sci., Singapore, 1990), p. 560
M.I. Eides, H. Grotch, V.A. Shelyuto, Theory of Light Hydrogenic Bound States (Springer, Berlin, Heidelberg, New York, 2007)
C.E. Carlson, M. Vanderhaeghen, Phys. Rev. A 84, 020102 (2011)
M.C. Birse, J.A. McGovern, Eur. Phys. J. A 48, 120 (2012)
A.A. Krutov, A.P. Martynenko, G.A. Martynenko, R.N. Faustov, JETP 120, 73 (2015)
C.E. Carlson, M. Gorchtein, M. Vanderhaeghen, Phys. Rev. A 89, 022504 (2014)
A.P. Martynenko, R.N. Faustov, Phys. At. Nucl. 67, 457 (2004)
D.A. Owen, Phys. Rev. D 42, 3534 (1990) [Erratum 46, 4782 (1992)]
D.A. Owen, Found. Phys. 24, 273 (1994)
M. Halpert, D.A. Owen, J. Phys. G 20, 51 (1994)
V.B. Berestetskii, E.M. Lifshitz, L.P. Pitaevskii, in Quantum electrodynamics, Course of theoretical physics, edited by L.D. Landau, E.M. Lifshitz (Pergamon Press, Oxford, 1982), Vol. 4
K. Pachucki, S.G. Karshenboim, J. Phys. B 28, L221 (1995)
V.A. Shelyuto, E.Y. Korzinin, S.G. Karshenboim, Phys. Rev. D 97, 096016 (2018)
I.B. Khriplovich, A.I. Milstein, R.A. Senkov, Phys. Lett. A221, 370 (1996)
I.B. Khriplovich, A.I. Milstein, R.A. Senkov, JETP 84, 1054 (1997)
S.G. Karshenboim, E.Yu. Korzinin, V.A. Shelyuto, V.G. Ivanov, J. Phys. Chem. Ref. Data 44, 031202 (2015)
S.G. Karshenboim, E.Yu. Korzinin, V.G. Ivanov, V.A. Shelyuto, Phys. Rev. D 91, 073003 (2015)
F. Rohrlich, Phys. Rev. 80, 666 (1950)
A. Salam, Phys. Rev. 82, 217 (1951)
A. Salam, Phys. Rev. 84, 426 (1951)
S.S. Schweber, H.A. Bethe, F. de Hoffmann, in Mesons and Fields (Row, Peterson and Company, Evanston, 1955), Vol. 1
S.S. Schweber, An introduction to relativistic quantum field theory (Dover, Mineola, 2005)
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Shelyuto, V.A., Korzinin, E.Y. & Karshenboim, S.G. Subtractions and the effective Salpeter term for the Lamb shift in muonic atoms with the nuclear spin I ≠ 1∕2. Eur. Phys. J. D 73, 23 (2019). https://doi.org/10.1140/epjd/e2018-90467-1
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DOI: https://doi.org/10.1140/epjd/e2018-90467-1