Abstract
The effective interaction ΔUAMM of the anomalous magnetic moment (AMM) of an electron with the Coulomb field of an extended nucleus is analyzed. As soon as the q2 dependence of the electron formfactor F2(q2)is taken into account from the beginning, the AMM is found to be dynamically screened at small distances of r ≪ 1/m. The ΔUAMM effects on the low-lying electronic levels of a superheavy extended nucleus with Zα > 1are analyzed using the nonperturbative approach. The growth rate of the ΔUAMM contribution with increasing Z is shown to be essentially nonmonotonic. At the same time, the energy shifts of electronic levels in the vicinity of the threshold of the lower continuum monotonically decrease in the region Z ≫Zcr,1s. The latter result is generalized to the whole self-energy contribution to energy shifts of electronic levels, thus also referring to the possible behavior of QED radiative effects with virtual-photon exchange, considered beyond the framework of the perturbative expansion in Zα.
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References
A. O. Barut and J. Kraus, “Resonances in e+e– system due to anomalous magnetic moment interactions,” Phys. Lett. B 59, 175–178 (1975).
K. Geiger, J. Reinhardt, B. Muller, and W. Greiner, “Magnetic moment interactions in the e–e+ system,” Zeitschr. Phys. A: At. Nucl. 329, 77–88 (1988).
A. O. Barut, “The electron-positron system at short distances,” Zeitschr. Phys. A: At. Nucl. 336, 317–320 (1990).
J. R. Reitz and F. J. Mayer, “New electromagnetic bound states,” J. Math. Phys. 41, 4572–4581 (2000).
W. Greiner, B. Mueller, and J. Rafelski, Quantum Electrodynamics of Strong Fields, 2nd ed. (Springer, Berlin, 1985).
V. S. Popov, “Critical charge in quantum electrodynamics,” Phys. At. Nucl. 64, 367–392 (2001).
R. Ruffini, G. Vereshchagin, and S. S. Xue, “Electronpositron pairs in physics and astrophysics: from heavy nuclei to black holes,” Phys. Rep. 487, 1–140 (2010); arXiv:0910.0974 [astro-ph.HE].
J. Rafelski, J. Kirsch, B. Mueller, J. Reinhardt, and W. Greiner, “Probing QED vacuum with heavy ions,” arXiv:1604.08690 (2016).
P. Schwerdtfeger, L. F. Pasteka, A. Punnett, and P. O. Bowman, “Relativistic and quantum electrodynamic effects in superheavy elements,” Nucl. Phys. A 944, 551–577 (2015).
K. A. Sveshnikov and D. I. Khomovskii, “High Z effects in accounting for radiative component of the electron magnetic moment in hydrogen-like atoms,” Phys. Part. Nucl. Lett. 10, 119–131 (2013).
A. Davydov, K. Sveshnikov, and Y. Voronina, “Vacuum energy of one-dimensional supercritical Dirac-Coulomb system,” Int. J. Mod. Phys. A 32, 1750054 (2017).
Y. Voronina, A. Davydov, and K. Sveshnikov, “Nonperturbative effects of vacuum polarization for the quasi-one-dimensional Dirac-Coulomb system with Z > Zcr,” Phys. Part. Nucl. Lett. 14, 698–712 (2017).
Y. Voronina, A. Davydov, and K. Sveshnikov, “Vacuum effects for one-dimensional “hydrogen atom” with Z > Zcr,” Theor. Math. Phys. 193, 1647–1674 (2017).
B. Lautrup, “The short distance behaviour of the anomalous magnetic moment of the electron,” Phys. Lett. B 62, 103–104 (1976).
A. O. Barut and J. Kraus, “Form-factor corrections to superpositronium and short-distance behavior of the magnetic moment of the electron,” Phys. Rev. D: Part. Fields 16, 161–164 (1977).
C. Itzykson and J. B. Zuber, Quantum Field Theory (McGraw-Hill, New York, 1980).
R. Barbieri, J. A. Mignaco, and E. Remiddi, “Electron form factors up to fourth order. I,” Nuovo Cim. A 11, 824–864 (1972).
H. Bateman and A. Erdelyi, Higher Transcendental Functions (McGraw-Hill, New York, 1953), Vols. 1,2.
G. Soff, P. Schlüter, B. Müller, and W. Greiner, “Selfenergy of electrons in critical fields,” Phys. Rev. Lett. 48, 1465–1468 (1982).
P. J. Mohr, G. Plunien, and G. Soff, “QED corrections in heavy atoms,” Phys. Rep. 293, 227–369 (1998).
P. J. Mohr, “Self-energy radiative corrections in hydrogen-like systems,” Ann. Phys. (N.Y.) 88, 26–51 (1974).
P. J. Mohr, “Self-energy of the n = 2 states in a strong Coulomb field,” Phys. Rev. A 26, 2338–2354 (1982).
P. J. Mohr and Y. K. Kim, “Self-energy of excited states in a strong Coulomb field,” Phys. Rev. A 45, 2727–2735 (1992).
W. R. Johnson and G. Soff, “The lamb shift in hydrogen-like atoms, 1 = Z = 110,” At. Data Nucl. Data Tables 33, 405–446 (1985).
V. A. Yerokhin and V. M. Shabaev, “Lamb shift of n = 1 and n = 2 states of hydrogen-like atoms, 1 = Z = 110,” J. Phys. Chem. Ref. Data 44, 033103 (2015).
K. T. Cheng and W. R. Johnson, “Self-energy corrections to the K-electron binding in heavy and superheavy atoms,” Phys. Rev. A 14, 1943–1948 (1976).
A. O. Barut and J. Kraus, “Relativistic formula for the magnetic part of the Lamb shift and its Z dependence,” Phys. Scr. 25, 561 (1982).
K. A. Sveshnikov and D. I. Khomovsky, “Perturbativity and nonperturbativity in large-Z effects for hydrogenlike atoms,” Moscow Univ. Phys. Bull. 71, 465–475 (2016).
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Original Russian Text © A.A. Roenko, K.A. Sveshnikov, 2018, published in Pis’ma v Zhurnal Fizika Elementarnykh Chastits i Atomnogo Yadra, 2018.
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Roenko, A.A., Sveshnikov, K.A. Dynamical screening of AMM and QED effects for large-Z hydrogen-like atoms. Phys. Part. Nuclei Lett. 15, 20–28 (2018). https://doi.org/10.1134/S1547477118010156
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DOI: https://doi.org/10.1134/S1547477118010156