Skip to main content

QED Effects and Challenges

  • Reference work entry
  • First Online:
Handbook of Relativistic Quantum Chemistry

Abstract

Quantum electrodynamics (QED) is the most accurate and the best confirmed theory in modern physics. This chapter is devoted to the description of the QED effects in atoms and molecules. Starting from the famous Lamb’s experiment with hydrogen, we finish with the most recent experiments with heavy ions. We will demonstrate the cases where the QED effects are extremely important for the comparison of the theoretical predictions with the experiment. Finally, we will provide brief review of the most important QED challenges at present.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 599.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 699.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. Dirac PAM (1928) The Quantum Theory of the Emission and Absorption of Radiation. Proc R Soc Lond Ser A 117:610

    Article  Google Scholar 

  2. Dirac PAM (1929) The Quantum Theory of the Electron. Proc R Soc Lond Ser A 126:360

    Article  Google Scholar 

  3. Dirac PAM (1931) A Theory of Electrons and Protons. Proc R Soc Lond Ser A 133:60

    Article  Google Scholar 

  4. Anderson CD (1933) The Positive Electron. Phys Rev 43:491

    Article  CAS  Google Scholar 

  5. Lamb WE Jr, Retherford RC (1947) Fine structure of the hydrogen atom by a microwave method. Phys Rev 72:241

    Article  CAS  Google Scholar 

  6. Tiselius A (1964) Nobel lectures, physics 1942–1962. Elsevier, Amsterdam

    Google Scholar 

  7. Houston WV (1937) A New Method of Analysis of the Structure of H α and D α . Phys Rev 51:446

    Article  CAS  Google Scholar 

  8. Williams RC (1938) The Fine Structures of H α and D α Under Varying Discharge Conditions. Phys Rev 54:558

    Article  CAS  Google Scholar 

  9. Bethe HA (1947) The electromagnetic shift of energy levels. Phys Rev 72:339

    Article  CAS  Google Scholar 

  10. Welton TA (1948) Some Observable Effects of the Quantum-Mechanical Fluctuations of the Electromagnetic Field. Phys Rev 74:1157

    Article  CAS  Google Scholar 

  11. Schweber SS (1994) QED and the men who made it: Dyson, Feynman, Schwinger, and Tomonaga. Princeton series in physics. Princeton University Press, Princeton

    Google Scholar 

  12. Kroll NM, Lamb WE Jr (1949) On the self-energy of a bound electron. Phys Rev 75:388

    Article  CAS  Google Scholar 

  13. Fukuda H, Miyamoto Y, Tomonaga S (1949) A Self-Consistent Subtraction Method in the Quantum Field Theory. Prog Theor Phys 4:47

    Article  Google Scholar 

  14. Uehling EA (1935) Polarization Effects in the Positron Theory. Phys Rev 48:55

    Article  CAS  Google Scholar 

  15. Feynman RP (1949) Space-time approach to quantum electrodynamics. Phys Rev 76:769

    Article  Google Scholar 

  16. Desiderio AM, Johnson WR (1971) Lamb Shift and Binding Energies of K Electrons in Heavy Atoms. Phys Rev A 3:1267

    Article  Google Scholar 

  17. Mohr PJ (1974) Self-Energy Radiative Corrections in Hydrogen-Like Systems. Ann Phys (New York) 88:26

    Article  CAS  Google Scholar 

  18. Mohr PJ (1974) Numerical Evaluation of the 1S1∕2-State Radiative Level Shift. Ann Phys (New York) 88:52

    Article  Google Scholar 

  19. Soff G, Mohr P (1988) Vacuum polarization in a strong external field. Phys Rev A 38:5066

    Article  CAS  Google Scholar 

  20. Manakov NL, Nekipelov AA, Fainshtein AG (1989) Vacuum polarization by a strong coulomb field and its contribution to the spectra of multiply-charged ions. Zh Eksp Teor Fiz 95:1167 [Sov Phys JETP 68:673 (1989)]

    Google Scholar 

  21. Yerokhin VA, Shabaev VM (2001) Two-loop self-energy correction in H-like ions. Phys Rev A 64:062507

    Article  Google Scholar 

  22. Shabaev VM (1993) Schrödinger-like equation for the relativistic few-electron atom. J Phys B 26:4703

    Article  CAS  Google Scholar 

  23. Lindgren I, Persson H, Salomonson S, Karasiev V, Labzowsky L, Mitrushenkov A, Tokman M (1993) Second-order QED corrections for few-electron heavy ions: reducible Breit-Coulomb correction and mixed self-energy–vacuum polarization correction. J Phys B 26:L503

    Article  CAS  Google Scholar 

  24. Lindgren I, Persson H, Salomonson S, Sunnergren P (1995) QED Calculations on Two- and Three-Electron Ions. Physica Scripta T59:179

    Article  CAS  Google Scholar 

  25. Artemyev AN, Beier T, Plunien G, Shabaev VM, Soff G, Yerokhin VA (1999) Vacuum polarization screening corrections to the energy levels of lithiumlike ions. Phys Rev A 60:45

    Article  CAS  Google Scholar 

  26. Yerokhin VA, Artemyev AN, Beier T, Plunien G, Shabaev VM, Soff G (1999) Two-electron self-energy corrections to the 2p 1∕2 − 2s transition energy in Li-like ions. Phys Rev A 60:3522

    Article  CAS  Google Scholar 

  27. Yerokhin VA, Artemyev AN, Shabaev VM, Sysak MM, Zherebtsov OM, Soff G (2000) Two-Photon Exchange Corrections to the 2p 1∕2 − 2s Transition Energy in Li-Like High-Z Ions. Phys Rev Lett 85:4699

    Article  CAS  Google Scholar 

  28. Sapirstein J, Cheng KT (2001) Determination of the two-loop Lamb shift in lithiumlike bismuth. Phys Rev A 64:022502

    Article  Google Scholar 

  29. Artemyev AN, Shabaev VM, Yerokhin VA, Plunien G, Soff G (2005) QED calculations of the n = 1 and n = 2 energy levels in He-like ions. Phys Rev A 71:062104

    Article  Google Scholar 

  30. Artemyev AN, Shabaev VM, Tupitsyn II, Plunien G, Surzhykov A, Fritzsche S (2013) Ab initio calculations of the 2p 3∕2 − 2p 1∕2 fine-structure splitting in boronlike ions. Phys Rev A 88:032518

    Article  Google Scholar 

  31. Malyshev AV, Volotka AV, Glazov DA, Tupitsyn II, Shabaev VM, Plunien G (2014) QED calculation of the ground-state energy of berylliumlike ions. Phys Rev A 90:062517

    Article  Google Scholar 

  32. Kozhedub YS, Andreev OV, Shabaev VM, Tupitsyn II, Brandau C, Kozhuharov C, Plunien G, Stöhlker T (2008) Nuclear deformation effect on the binding energies in heavy ions. Phys Rev A 77:032501

    Article  Google Scholar 

  33. Mohr PJ, Plunien G, Soff G (1998) QED corrections in heavy atoms. Phys Rep 293:227

    Article  CAS  Google Scholar 

  34. Yerokhin VA, Indelicato P, Shabaev VM (2003) Evaluation of the two-loop self-energy correction to the ground state energy of H-like ions to all orders in (Z α). Eur Phys J D 25:203

    Article  CAS  Google Scholar 

  35. Artemyev AN, Shabaev VM, Yerokhin VA (1995) Relativistic nuclear recoil corrections to the energy levels of hydrogenlike and high-Z lithiumlike atoms in all orders in α Z. Phys Rev A 52:1884

    Article  Google Scholar 

  36. Plunien G, Soff G (1995) Nuclear polarization contribution to the Lamb shift in actinide nuclei. Phys Rev A 51:1119

    Article  CAS  Google Scholar 

  37. Nefiodov AV, Labzowsky LN, Plunien G, Soff G (1996) Nuclear polarization effects in spectra of multicharged ions. Phys Lett A 222:227

    Article  CAS  Google Scholar 

  38. Gumberidze A, Bosch F, Bräuning-Demian A, Hagmann S, Kühl T, Liesen D, Schuch R, Stöhlker T (2005) Atomic physics with highly-charged heavy ions at the GSI future facility: The scientific program of the SPARC collaboration. Nucl Instrum Methods Phys Res Sect B: Beam Interact Mater Atoms 233:28. Fast ion-atom collisions – proceedings of the eighth workshop on fast ion-atom collisions, eighth workshop on fast ion-atom collisions

    Google Scholar 

  39. Yerokhin VA, Indelicato P, Shabaev VM (2006) Nonperturbative Calculation of the Two-Loop Lamb Shift in Li-Like Ions. Phys Rev Lett 97:253004

    Article  CAS  Google Scholar 

  40. Beiersdorfer P, Chen H, Thorn DB, Träbert E (2005) Measurement of the Two-Loop Lamb Shift in Lithiumlike U89+. Phys Rev Lett 95:233003

    Article  CAS  Google Scholar 

  41. Schweppe J, Belkacem A, Blumenfeld L, Claytor N, Feinberg B, Gould H, Kostroun VE, Levy L, Misawa S, Mowat JR, Prior MH (1991) Measurement of the Lamb Shift in Lithiumlike Uranium (U89+). Phys Rev Lett 66:1434

    Article  CAS  Google Scholar 

  42. Brandau C, Kozhuharov C, Müller A, Shi W, Schippers S, Bartsch T, Böhm S, Böhme C, Hoffknecht A, Knopp H, Grün N, Scheid W, Steih T, Bosch F, Franzke B, Mokler PH, Nolden F, Steck M, Stöhlker T, Stachura Z (2003) Precise Determination of the 2s 1∕2-2p 1∕2 Splitting in Very Heavy Lithiumlike Ions Utilizing Dielectronic Recombination. Phys Rev Lett 91:073202

    Article  CAS  Google Scholar 

  43. Häffner H, Beier T, Hermanspahn N, Kluge HJ, Quint W, Stahl S, Verdú J, Werth G (2000) High-Accuracy Measurement of the Magnetic Moment Anomaly of the Electron Bound in Hydrogenlike Carbon. Phys Rev Lett 85:5308

    Article  Google Scholar 

  44. Verdú J, Djekić S, Stahl S, Valenzuela T, Vogel M, Werth G, Beier T, Kluge HJ, Quint W (2004) Electronic g Factor of Hydrogenlike Oxygen16O7+. Phys Rev Lett 92:093002

    Article  Google Scholar 

  45. Sturm S, Wagner A, Schabinger B, Zatorski J, Harman Z, Quint W, Werth G, Keitel CH, Blaum K (2011) g Factor of Hydrogenlike28Si13+. Phys Rev Lett 107:023002

    Google Scholar 

  46. Beier T, Häffner H, Hermanspahn N, Karshenboim SG, Kluge HJ, Quint W, Stahl S, Verdú J, Werth G (2001) A new determination of the electron’s massNuclear Mass Corrections to the Electron g Factor. Phys Rev Lett 88:011603

    Article  Google Scholar 

  47. Grotch H (1970) Nuclear Mass Corrections to the Electron g Factor. Phys Rev Lett 24:39

    Article  CAS  Google Scholar 

  48. Beier T (2000) The g j factor of a bound electron and the hyperfine structure splitting in hydrogenlike ions. Phys Rep 339:79

    Article  CAS  Google Scholar 

  49. Martynenko AP, Faustov RN (2001) The g Factors of Bound Particles in Quantum Electrodynamics. Zh Eksp Teor Fiz 120:539. [JETP 93(3):471–476 (2001)]

    Google Scholar 

  50. Shabaev VM, Yerokhin VA (2002) Recoil Correction to the Bound-Electron g Factor in H-Like Atoms to All Orders in α Z. Phys Rev Lett 88:091801

    Article  CAS  Google Scholar 

  51. Yerokhin VA, Indelicato P, Shabaev VM (2002) Self-Energy Correction to the Bound-Electron g Factor in H-like Ions. Phys Rev Lett 89:143001

    Article  CAS  Google Scholar 

  52. Pachucki K, Jentschura UD, Yerokhin VA (2004) Nonrelativistic QED Approach to the Bound-Electron g Factor. Phys Rev Lett 93:150401

    Article  Google Scholar 

  53. Pachucki K, Jentschura UD, Yerokhin VA (2005) Erratum: Nonrelativistic QED Approach to the Bound-Electron g Factor Phys Rev Lett 94:229902

    Google Scholar 

  54. Lee RN, Milstein AI, Terekhov IS, Karshenboim SG (2005) Virtual light-by-light scattering and the g factor of a bound electron. Phys Rev A 71:052501

    Article  Google Scholar 

  55. Pachucki K, Czarnecki A, Jentschura UD, Yerokhin VA (2005) Complete two-loop correction to the bound-electron g factor. Phys Rev A 72:022108

    Article  Google Scholar 

  56. Mohr PJ, Taylor BN (2005) CODATA recommended values of the fundamental physical constants: 2002. Rev Mod Phys 77:1

    Article  CAS  Google Scholar 

  57. Sturm S, Kohler F, Zatorski J, Wagner A, Harman Z, Werth G, Quint W, Keitel CH, Blaum K (2014) High-precision measurement of the atomic mass of the electron. Nature 506:467

    Article  CAS  Google Scholar 

  58. Shabaev VM, Glazov DA, Oreshkina NS, Volotka AV, Plunien G, Kluge HJ, Quint W (2006) g-Factor of Heavy Ions: A New Access to the Fine Structure Constant. Phys Rev Lett 96:253002

    Google Scholar 

  59. Draganić I, López-Urrutia JRC, DuBois R, Fritzsche S, Shabaev VM, Orts RS, Tupitsyn II, Zou Y, Ullrich J (2003) High precision wavelength measurements of QED-sensitive forbidden transitions in highly charged argon ions. Phys Rev Lett 91:183001

    Article  Google Scholar 

  60. Mäckel V, Klawitter R, Brenner G, López-Urrutia JRC, Ullrich J, Physica Scripta T156:014004 (2013) Laser spectroscopy of highly charged argon at the Heidelberg electron beam ion trap

    Google Scholar 

  61. Artemyev AN, Shabaev VM, Tupitsyn II, Plunien G, Yerokhin VA (2007) QED Calculation of the 2p 3∕2 − 2p 1∕2 Transition Energy in Boronlike Argon. Phys Rev Lett 98:173004

    Article  Google Scholar 

  62. Shabaev VM, Tupitsyn II, Yerokhin VA (2013) Model operator approach to the Lamb shift calculations in relativistic many-electron atoms. Phys Rev A 88:012513

    Article  Google Scholar 

  63. Korobov VI, Hilico L, Karr JP (2014) Theoretical transition frequencies beyond 0.1 ppb accuracy in H2 +, HD+, and antiprotonic helium. Phys Rev A 89:032511

    Google Scholar 

  64. Pieper W, Greiner W (1969) Interior electron shells in superheavy nuclei. Zeitschrift für Physik A Hadrons and Nuclei 218:327

    Article  CAS  Google Scholar 

  65. Soff G, Müller B, Greiner W (1978) Spectroscopy of Electronic States in Superheavy Quasimolecules. Phys Rev Lett 40:540

    Article  CAS  Google Scholar 

  66. Tupitsyn II, Kozhedub YS, Shabaev VM, Deyneka GB, Hagmann S, Kozhuharov C, Plunien G, Stöhlker T (2010) Relativistic calculations of the charge-transfer probabilities and cross sections for low-energy collisions of H-like ions with bare nuclei. Phys Rev A 82:042701

    Article  Google Scholar 

  67. Artemyev AN, Surzhykov A, Indelicato P, Plunien G, Stöhlker T (2010) Finite basis set approach to the two-centre Dirac problem in Cassini coordinates. JPB 43:235207

    Article  Google Scholar 

  68. Müller-Nehler U, Soff G (1994) Electron Excitations in Superheavy Quasimolecules. Phys Rep 246:101

    Article  Google Scholar 

  69. Henning W (ed) (2001) FAIR conceptual design report: an international accelerator facility for beams of ions and antiprotons. GSI

    Google Scholar 

  70. McConnell SR, Artemyev AN, Mai M, Surzhykov A (2012) Solution of the two-center time-dependent Dirac equation in spherical coordinates: Application of the multipole expansion of the electron-nuclei interaction. Phys Rev A 86:052705

    Article  Google Scholar 

  71. Tupitsyn II, Kozhedub YS, Shabaev VM, Bondarev AI, Deyneka GB, Maltsev IA, Hagmann S, Plunien G, Stöhlker T (2012) Relativistic calculations of the K-K charge transfer and K-vacancy production probabilities in low-energy ion-atom collisions. Phys Rev A 85:032712

    Article  Google Scholar 

  72. Soff G, Müller B, Rafelski J (1974) Precise Values for Critical fields in Quantum Electrodynamics. Z Naturforsch A 29:1267

    Article  CAS  Google Scholar 

  73. Soff G, Schlüter P, Müller B, Greiner W (1982) Self-Energy of Electrons in Critical Fields. Phys Rev Lett 48:1465

    Article  CAS  Google Scholar 

  74. Persson H, Lindgren I, Salomonson S, Sunnergren P (1993) Accurate vacuum polarization contributions. Phys Rev A 48:2772

    Article  CAS  Google Scholar 

  75. Artemyev AN, Surzhykov A (2015) Quantum electrodynamical corrections to energy levels of diatomic quasimolecules. Phys Rev Lett 114:243004

    Article  CAS  Google Scholar 

Download references

Acknowledgements

Stimulating discussions with Prof. V. M. Shabaev and Prof. P. Indelicato are gratefully acknowledged.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Anton N. Artemyev .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer-Verlag Berlin Heidelberg

About this entry

Cite this entry

Artemyev, A. (2017). QED Effects and Challenges. In: Liu, W. (eds) Handbook of Relativistic Quantum Chemistry. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40766-6_26

Download citation

Publish with us

Policies and ethics