Abstract
The Lamb shift (2P 1/2-2S 1/2) in muonic helium ions (μ 32 )+, (μ2/4He)+ is calculated taking into account the contributions of the order of α3, α4, α5, and α6. Special attention is paid to corrections for the polarization of the vacuum, as well as the structure and recoil of the nucleus. Numerical values 1259.8583 meV ((μ 32 He)+) and 1379.1107 meV ((μ 42 He)+) obtained for the shifts can be considered reliable estimates when compared to the experimental data of the CREMA collaboration.
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P. J. Mohr, B. N. Taylor, and D. B. Newell, Rev. Mod. Phys. 84, 1533 (2012).
S. G. Karshenboim, Phys.—Usp. 56(9), 883 (2013); S. G. Karshenboim, Ann. Phys. (Weinheim) 525, 472 (2013).
R. Pohl, A. Antognini, F. Nez, F. D. Amaro, F. Biraben, J. M. R. Cardoso, D. S. Covita, A. Dax, S. Dhawan, L. M. P. Fernandes, A. Giesen, T. Graf, T. W. Hänsch, P. Indelicato, L. Julien, C.-Y. Kao, P. Knowles, 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, and F. Kottmann, Nature (London) 466, 213 (2010); 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. Mulhauser, T. Nebel, F. Nez, J. M. F. Dos Santos, K. Schuhmann, D. Taqqu, J. F. C. A. Veloso, A. Voss, and R. Pohl, Can. J. Phys. 89, 47 (2011); A. Antognini, He 4 2 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, C.-Y. 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, and R. Pohl, Science (Washington) 339, 417 (2013); R. Pohl, R. Gilman, G. A. Miller, and K. Pachucki, Annu. Rev. Nucl. Part. Sci. 63, 175 (2013).
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, and R. Pohl, Hyperfine Interact. 212, 195 (2012); A. Antognini, F. Kottmann, F. Biraben, P. Indelicato, F. Nez, and R. Pohl, Ann. Phys. 331, 127 (2013).
M. I. Eides, H. Grotch, and V. A. Shelyuto, Phys. Rep. 342, 62 (2001); M. I. Eides, H. Grotch, and V. A. Shelyuto, Theory of Light Hydrogenic Bound States (Springer-Verlag, Berlin, 2007).
E. Borie, Z. Phys. A: At. Nucl. 275, 347 (1975); E. Borie and G. A. Rinker, Phys. Rev. A: At., Mol., Opt. Phys. 18, 324 (1978); E. Borie and G. A. Rinker, Rev. Mod. Phys. 54, 67 (1982).
E. Borie, Phys. Rev. A: At., Mol., Opt. Phys. 72, 052511 (2005); E. Borie, Phys. Rev. A: At., Mol., Opt. Phys. 71, 032508 (2005); E. Borie, Ann. Phys. (New York) 327, 733 (2012).
K. Pachucki, Phys. Rev. A: At., Mol., Opt. Phys. 54, 1994 (1996); K. Pachucki, Phys. Rev. A: At., Mol., Opt. Phys. 60, 3593 (1999); K. Pachucki, Phys. Rev. Lett. 106, 193007 (2011); A. Veitia and K. Pachucki, Phys. Rev. A: At., Mol., Opt. Phys. 69, 042501 (2004).
I. B. Khriplovich and A. I. Milstein, J. Exp. Theor. Phys. 98, 181 (2004); A. I. Milstein, I. B. Khriplovich, and S. S. Petrosyan, J. Exp. Theor. Phys. 82, 616 (1996).
C. E. Carlson, V. Nazaryan, and K. Griffioen, Phys. Rev. A: At., Mol., Opt. Phys. 83, 042509 (2011); C. E. Carlson, V. Nazaryan, and K. Griffioen, Phys. Rev. A: At., Mol., Opt. Phys. 78, 022517 (2008); C. E. Carlson and M. Vanderhaeghen, Phys. Rev. A: At., Mol., Opt. Phys. 84, 020102(R) (2011); C. E. Carlson, M. Gorchtein, and M. Vanderhaeghen, Phys. Rev. A: At., Mol., Opt. Phys. 89, 022504 (2014).
J. L. Friar, Ann. Phys. 122, 151 (1979); J. L. Friar, J. Martorell, and D. W. L. Sprung, Phys. Rev. A: At., Mol., Opt. Phys. 56, 4579 (1997); J. L. Friar and G. L. Payne, Phys. Lett. B 618, 68 (2005); J. L. Friar, Phys. Rev. C: Nucl. Phys. 88, 034003 (2013).
U. D. Jentschura, Ann. Phys. 326, 500 (2011); U. D. Jentschura, Phys. Rev. A: At., Mol., Opt. Phys. 84, 012505 (2011); U. D. Jentschura, Eur. Phys. J. D 61, 7 (2011).
P. Indelicato, Phys. Rev. A: At., Mol., Opt. Phys. 87, 022501 (2013).
A. P. Martynenko and R. N. Faustov, J. Exp. Theor. Phys. 88(4), 672 (1999); A. P. Martynenko and R. N. Faustov, J. Exp. Theor. Phys. 98 (1), 39 (2004); R. N. Faustov and A. P. Martynenko, Phys. Rev. A: At., Mol., Opt. Phys. 67, 052506 (2003); R. N. Faustov and A. P. Martynenko, Phys. At. Nucl. 67, 457 (2004); A. P. Martynenko, J. Exp. Theor. Phys. 106 (4), 690 (2008); A. P. Martynenko, J. Exp. Theor. Phys. 101 (6), 1021 (2005).
G. W. F. Drake and L. L. Byer, Phys. Rev. A: At., Mol., Opt. Phys. 32, 713 (1985); A. H. Gomes, V. A. Kostelecky, and A. J. Vargas, arXiv:1407:7748 [hep-ph].
D. Nevado and A. Pineda, Phys. Rev. C: Nucl. Phys. 77, 035202 (2008); A. Pineda, Phys. Rev. C: Nucl. Phys. 67, 025201 (2003); A. Pineda, Phys. Rev. C: Nucl. Phys. 71, 065205 (2005).
E. Yu. Korzinin, V. G. Ivanov, and S. G. Karshenboim, Phys. Rev. D: Part., Fields, Gravitation, Cosmol. 88, 125019 (2013); S. G. Karshenboim, V. G. Ivanov, E. Yu. Korzinin, and V. A. Shelyuto, Phys. Rev. A: At., Mol., Opt. Phys. 81, 060501 (2010); S. G. Karshenboim, E. Yu. Korzinin, and V. G. Ivanov, JETP Lett. 88 (10), 641 (2008).
A. P. Martynenko, Phys. Rev. A: At., Mol., Opt. Phys. 76, 012505 (2007).
A. P. Martynenko, Phys. Rev. A: At., Mol., Opt. Phys. 71, 022506 (2005); A. P. Martynenko, Phys. At. Nucl. 69, 1309 (2006); A. P. Martynenko, Phys. At. Nucl. 71, 125 (2008); A. A. Krutov and A. P. Martynenko, Phys. Rev. A: At., Mol., Opt. Phys. 84, 052514 (2011); A. P. Martynenko, and E. N. Elekina, Phys. At. Nucl. 73 (12), 2074 (2010); A. P. Martynenko, A. A. Krutov, and R. N. Shamsutdinov, Phys. At. Nucl. 77, 786 (2014).
R. N. Faustov, A. P. Martynenko, G. A. Martynenko, and V. V. Sorokin, Phys. Lett. B 733, 354 (2014); R. N. Faustov, A. P. Martynenko, G. A. Martynenko, and V. V. Sorokin, Phys. Rev. A: At., Mol., Opt. Phys. 90, 012520 (2014).
L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics, Vol. 4: V. B. Berestetskii, E. M. Lifshitz, and L. P. Pitaevskii, Quantum Electrodynamics (Fizmatlit, Moscow, 2006; Butterworth-Heinemann, Oxford, 2007).
K. Pachucki and S. G. Karshenboim, J. Phys. B: At., Mol. Opt. Phys. 28, L221 (1995).
T. Kinoshita and M. Nio, Phys. Rev. Lett. 62, 3240 (1999); T. Kinoshita and M. Nio, Phys. Rev. D: Part. Fields 60, 053008 (1999).
S. G. Karshenboim, V. G. Ivanov, E. Yu. Korzinin, and V. A. Shelyuto, JETP Lett. 92(1), 8 (2010).
E. H. Wichmann and N. M. Kroll, Phys. Rev. 101, 843 (1956).
P. J. Mohr, G. Plunien, and G. Soff, Phys. Rep. 293, 228 (1998).
S. A. Zapryagaev, N. L. Manakov, and V. G. Pal’chikov, The Theory of Multiply Charged Ions with One and Two Electrons (Energoatomizdat, Moscow, 1985) [in Russian].
H. F. Hameka, J. Chem. Phys. 47, 2728 (1967).
L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics, Vol. 3: Quantum Mechanics: Non-Relativistic Theory (Butterworth-Heinemann, Oxford, 2005; Fizmatlit, Moscow, 2008).
I. Sick, Phys. Lett. B 116, 212 (1982); D. C. Morton, Q. Wu, and G. W. F. Drake, Phys. Rev. C: Nucl. Phys. 73, 034502 (2006).
J. R. Sapirstein and D. R. Yennie, in Quantum Electrodynamics, Ed. by T. Kinoshita (World Scientific, Singapore, 1990), p. 560.
M. I. Eides and H. Grotch, Phys. Rev. A: At., Mol., Opt. Phys. 55, 3351 (1995); M. I. Eides and H. Grotch, Phys. Rev. A: At., Mol., Opt. Phys. 56, R2507 (1997).
G. P. Lepage, D. R. Yennie, and G. W. Erickson, Phys. Rev. Lett. 47, 1640 (1981).
R. Barbieri, M. Caffo, and E. Remiddi, Nuovo Cimento Lett. 7, 60 (1973).
E. Borie, Z. Phys. A: At. Nucl. 302, 187 (1981).
J. L. Friar, J. Martorell, and D. W. L. Sprung, Phys. Rev. A: At., Mol., Opt. Phys. 59, 4061 (1999).
R. N. Faustov and A. P. Martynenko, Eur. Phys. J. C 6, 1 (1999); A. P. Martynenko and R. N. Faustov, Phys. At. Nucl. 64 (7), 1282 (2001).
J. Bernabeu and C. Jarlskog, Nucl. Phys. B 75, 59 (1974); G. A. Rinker, Phys. Rev. A: At., Mol., Opt. Phys. 14, 18 (1976).
C. Ji, N. N. Dinur, S. Bacca, and N. Barnea, Phys. Rev. Lett. 111, 143402 (2013).
U. D. Jentschura and B. J. Wundt, Eur. Phys. J. D 65, 357 (2011).
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Original Russian Text © A.A. Krutov, A.P. Martynenko, G.A. Martynenko, R.N. Faustov, 2015, published in Zhurnal Eksperimental’noi i Teoreticheskoi Fiziki, 2015, Vol. 147, No. 1, pp. 85–104.
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Krutov, A.A., Martynenko, A.P., Martynenko, G.A. et al. Theory of the Lamb shift in muonic helium ions. J. Exp. Theor. Phys. 120, 73–90 (2015). https://doi.org/10.1134/S1063776115010033
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DOI: https://doi.org/10.1134/S1063776115010033