Skip to main content
SpringerLink
Log in

Probing QED Vacuum with Heavy Ions

  • Chapter
  • First Online:
New Horizons in Fundamental Physics

Part of the book series: FIAS Interdisciplinary Science Series ((FIAS))

Abstract

We recall how nearly half a century ago the proposal was made to explore the structure of the quantum vacuum using slow heavy-ion collisions. Pursuing this topic we review the foundational concept of spontaneous vacuum decay accompanied by observable positron emission in heavy-ion collisions and describe the related theoretical developments in strong fields QED.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
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

References

  1. O. (Oscar) Klein, Die Reflexion von Elektronen an einem Potentialsprung nach der relativistischen Dynamik von Dirac (translated: On reflection of electrons on a potential step in the context of Dirac’s relativistic dynamics). Z. f. Physik 53, 157 (1929)

    Google Scholar 

  2. G.E. Brown, W. Greiner, D.H. Wilkinson (those only contributing to the pertinent topic of panel discussion), Panel discussion: new directions, in nuclear spectroscopy, in Proceedings of the International Conference on Properties of Nuclear States, University of Montréal press, Montréal, 25–30 Aug 1969, pp. 605–630

    Google Scholar 

  3. W. Pieper, W. Greiner, Interior electron shells in superheavy nuclei. Z. f. Physik 218, 327 (1969)

    Article  ADS  Google Scholar 

  4. D. Rein, Über den Grundzustand überschwerer Atome, (translated: On the groundstate of superheavy atoms). Z. f. Physik 221, 423 (1969)

    Google Scholar 

  5. V.S. Popov, Critical charge in quantum electrodynamics. Phys. At. Nucl. 64, 367 (2001)

    Article  Google Scholar 

  6. J. Rafelski, Die Konsequenzen nichtlinearer elektromagnetischer Feldtheorie in überschweren Elementen, Diploma Thesis Institut für Theoretische Physik der Universität Frankfurt am Main, June 1971, http://inspirehep.net/record/1468114/files/Thesis-1971-Rafelski.pdf

  7. J. Rafelski, L.P. Fulcher, W. Greiner, Superheavy elements and an upper limit to the electric field strength. Phys. Rev. Lett. 31, 958 (1971)

    Article  ADS  Google Scholar 

  8. J. Rafelski, G. Soff, W. Greiner, Lower bound to limiting fields in nonlinear electrodynamics. Phys. Rev. A 7, 903 (1973)

    Article  ADS  Google Scholar 

  9. J. Rafelski, L.P. Fulcher, A. Klein, Fermions and bosons interacting with arbitrarily strong external fields. Phys. Rep. 38, 228 (1978)

    Article  ADS  Google Scholar 

  10. B. Müller, H. Peitz, J. Rafelski, W. Greiner, Solution of the Dirac equation for strong external fields. Phys. Rev. Lett. 28, 1235 (1972)

    Article  ADS  Google Scholar 

  11. B. Müller, J. Rafelski, W. Greiner, Electron shells in over-critical external fields. Z. f. Physik 257, 62 (1972)

    Google Scholar 

  12. U. Fano, Effects of configuration interaction on intensities and phase shifts. Phys. Rev. 124, 1866 (1961)

    Article  ADS  MATH  Google Scholar 

  13. B. Müller, J. Rafelski, W. Greiner, Auto-ionization of positrons in heavy-ion collisions. Z. Phys. 257, 183 (1972)

    Article  ADS  Google Scholar 

  14. S. Gershtein, Y. Zeldovich, Positron production during the mutual approach of heavy nuclei and the polarization of the vacuum. Sov. Phys. JETP 30, 358 (1970) (Zh. Eksp. Teor. Fiz. 57, 654 (1969))

    Google Scholar 

  15. Y.B. Zeldovich, V.S. Popov, Electronic structure of superheavy atoms. Soviet Phys. Uspekhi 14, 673 (1972)

    Google Scholar 

  16. J. Rafelski, B. Müller, W. Greiner, The charged vacuum in over-critical fields. Nucl. Phys. B 38, 585 (1974)

    Article  ADS  Google Scholar 

  17. B. Müller, Positron creation in superheavy quasi-molecules. Ann. Rev. Nucl. Sci. 26, 351 (1976)

    Article  ADS  Google Scholar 

  18. J. Reinhardt, W. Greiner, Quantum electrodynamics of strong fields. Rep. Prog. Phys. 40, 219 (1977)

    Article  ADS  Google Scholar 

  19. W. Greiner, B. Müller, J. Rafelski, Quantum Electrodynamics of Strong Fields (Springer, Heidelberg, 1985)

    Book  Google Scholar 

  20. J. Kirsch, B. Müller, J. Rafelski, Quantum Electrodynamics In Strong External Fields, GSI-81-5 (Darmstadt 1981), http://cds.cern.ch/record/129153, http://cds.cern.ch/record/129153/files/CM-P00067712.pdf

  21. J. Rafelski, B. Müller, Magnetic splitting of quasimolecular electronic states in strong fields. Phys. Rev. Lett. 36, 517 (1976)

    Article  ADS  Google Scholar 

  22. B. Müller, J. Rafelski, W. Greiner, Electron wave functions in over-critical electrostatic potentials. Nuovo Cimento A 18, 551 (1973)

    Article  ADS  Google Scholar 

  23. P.A.M. Dirac, Principles of Quantum Mechanics (Oxford University Press, Oxford, 1982)

    MATH  Google Scholar 

  24. See e.g. J.M. Jauch, F.Rohrlich, The Theory of Photons and Electrons, 2nd edn. (Springer, Heidelberg, 1976)

    Google Scholar 

  25. L. Fulcher, A. Klein, Stability of the vacuum and quantization of the electron-positron field for strong external fields. Phys. Rev. D 8, 2455 (1973)

    Article  ADS  Google Scholar 

  26. L. Fulcher, A. Klein, Remarks concerning a model field theory suggested by quantum electrodynamics in a strong electric field. Ann. Phys. 84, 335 (1974)

    Article  ADS  Google Scholar 

  27. J.S. Schwinger, On gauge invariance and vacuum polarization. Phys. Rev. 82, 664 (1951)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  28. E.H. Wichmann, N.M. Kroll, Vacuum polarization in a strong Coulomb field. Phys. Rev. 101, 843 (1956)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  29. M.L. Goldberger, K.M. Watson, Collision Theory (Wiley, New York, 1964)

    MATH  Google Scholar 

  30. G.W. Pratt, A generalized single-particle equation. Rev. Mod. Phys. 35, 502 (1963)

    Article  ADS  MathSciNet  Google Scholar 

  31. P.G. Reinhard, W. Greiner, H. Arenhovel, Electrons in strong external fields. Nucl. Phys. A 166, 173 (1971)

    Article  ADS  Google Scholar 

  32. L. Gomberoff, V. Tolmachev, Hartree-fock approximation in quantum electrodynamics. Phys. Rev. D 3, 1796 (1971)

    Article  ADS  Google Scholar 

  33. B. Müller, J. Rafelski, Stabilization of the charged vacuum created by very strong electrical fields in nuclear matter. Phys. Rev. Lett. 34, 349 (1975)

    Article  ADS  Google Scholar 

  34. R. Serber, Linear modifications in the Maxwell field equations. Phys. Rev. 48, 49 (1935)

    Article  ADS  MATH  Google Scholar 

  35. E.A. Uehling, Polarization effects in the positron theory. Phys. Rev. 48, 55 (1935)

    Article  ADS  MATH  Google Scholar 

  36. F.T. Porter, M.S. Freedman, Experimental atomic-electron binding energies in Fermium. Phys. Rev. Lett. 27, 293 (1971)

    Article  ADS  Google Scholar 

  37. G.A. Rinker-and, L. Wilets, Vacuum polarization in high-\(Z\), finite-size nuclei. Phys. Rev. Lett. 31, 1559 (1973)

    Article  ADS  Google Scholar 

  38. G.A. Rinker-and, L. Wilets, Vacuum polarization in strong, realistic electric fields. Phys. Rev. A 12, 748 (1975)

    Article  ADS  Google Scholar 

  39. M. Gyulassy, Nuclear size effects on vacuum polarization in muonic Pb. Phys. Rev. Lett. 32, 1393 (1974)

    Article  ADS  Google Scholar 

  40. M. Gyulassy, Vacuum polarization in heavy-ion collisions. Phys. Rev. Lett. 33, 921 (1974)

    Article  ADS  Google Scholar 

  41. M. Gyulassy, Higher order vacuum polarization for finite radius nuclei. Nucl. Phys. A 244, 497 (1975)

    Article  ADS  Google Scholar 

  42. J. Madsen, Universal charge-radius relation for subatomic and astrophysical compact objects. Phys. Rev. Lett. 100, 151102 (2008)

    Article  ADS  Google Scholar 

  43. A.B. Migdal, D.N. Voskresenskii, V.S. Popov, About vacuum charge distribution near supercharged nuclei. JETP Lett. 24), 163 (1976) (In Russian: Pisma Zh. Eksp. Teor. Fiz. 24, 186 (1976))

    Google Scholar 

  44. A.B. Migdal, V.S. Popov, D.N. Voskresensky, Distribution of vacuum charge near supercharged nuclei. Sov. Phys. JETP 45, 436 (1977) (In Russian: Zh. Eksp. Teor. Fiz. 72, 834 (1977))

    Google Scholar 

  45. J. Ferreirinho, R. Ruffini, S. Stella, On the relativistic Thomas-Fermi model. Phys. Lett. B 91, 314 (1980)

    Article  ADS  Google Scholar 

  46. R. Ruffini, L. Stella, Some comments on the relativistic Thomas-Fermi model and the Vallarta-Rosen equation. Phys. Lett. B 102, 442 (1981)

    Article  ADS  Google Scholar 

  47. G.W. Erickson, D.R. Yennie, Radiative level shifts, I. Formulation and lowest order Lamb shift. Ann. Phys. (NY) 35, 271 (1965)

    Google Scholar 

  48. G.W. Erickson, D.R. Yennie, Radiative level shifts II: Higher order contributions to the Lamb shift. Ann. Phys. (NY) 35, 447 (1965)

    Google Scholar 

  49. G.E. Brown, J.S. Langer, G.W. Schaefer, Lamb shift of a tightly bound electron. I. Method. Proc. Roy. Soc. A 251, 92 (1959)

    Article  ADS  MATH  Google Scholar 

  50. G.E. Brown, D.F. Mayers, Lamb shift of a tightly bound electron. II. Calculation for the K-Electron in Mercury. Proc. Roy. Soc. A 251, 105 (1959)

    Article  ADS  MATH  Google Scholar 

  51. G.W. Erickson, Improved Lamb-shift calculation for all values of \(Z\). Phys. Rev. Lett. 27, 780 (1971)

    Article  ADS  Google Scholar 

  52. A.M. Desiderio, W.R. Johnson, Lamb shift and binding energies of K electrons in heavy atoms. Phys. Rev. A 3, 1267 (1971)

    Article  ADS  Google Scholar 

  53. P. Mohr, Lamb shift in a strong Coulomb potential. Phys. Rev. Lett. 34, 1050 (1973)

    Article  ADS  Google Scholar 

  54. K.T. Cheng, W.R. Johnson, Self-energy corrections to the K-electron binding in heavy and superheavy atoms. Phys. Rev. A 14, 1943 (1976)

    Article  ADS  Google Scholar 

  55. I. Goidenko, L. Labzowsky, A. Nefiodov, G. Plunien, G. Soff, The second order electron selfenergy in hydrogen—like ions. Phys. Rev. Lett. 83, 2312 (1999)

    Article  ADS  Google Scholar 

  56. P. Indelicato, J.P. Santos, S. Boucard, J.-P. Desclaux, QED and relativistic corrections in superheavy elements. Eur. Phys. J. D 45, 155 (2007)

    Article  ADS  Google Scholar 

  57. J. Rafelski, B. Müller, W. Greiner, Superheavy electronic molecules. Lett. Nuovo Cim. 4, 469 (1972)

    Article  Google Scholar 

  58. J. Rafelski, B. Müller, W. Greiner, Spontaneous vacuum decay of supercritical nuclear composites. Z. Physik A 285, 49 (1978)

    Article  ADS  Google Scholar 

  59. J. Kirsch, W. Betz, J. Reinhardt, G. Soff, B. Müller, W. Greiner, K-X-ray spectrum of the Pb + Pb quasimolecules. Phys. Lett. B 72, 298 (1978)

    Google Scholar 

  60. R. Anholt, X rays from quasimolecules. Rev. Mod. Phys. 57, 995 (1985)

    Article  ADS  Google Scholar 

  61. B. Müller, J. Rafelski, W. Greiner, Solution of the Dirac equation with two Coulomb centers. Phys. Lett. B 47, 5 (1973)

    Article  ADS  Google Scholar 

  62. B. Müller, W. Greiner, Two-center Dirac equation. Z. Naturforsch. 31a, 1 (1976)

    Google Scholar 

  63. K. Smith, B. Müller, W. Greiner, Dynamical theory of intermediate molecular phenomena in heavy-ion scattering. J. Phys. B 8, 75 (1975)

    Article  ADS  Google Scholar 

  64. W. Betz, Ph.D. Dissertation, Elektronen in Superschweren Quasimoleculen (Univ. Frankfurt, 1980)

    Google Scholar 

  65. G. Soff, W. Greiner, W. Betz, B. Müller, Electrons in superheavy quasimolecules. Phys. Rev. A 20, 169 (1979)

    Article  ADS  Google Scholar 

  66. J. Rafelski, B. Müller, The critical distance in collisions of heavy-ions. Phys. Lett. B 65, 205 (1976)

    Article  ADS  Google Scholar 

  67. K.H. Wietschorke, Self-consistent determination of critical two-center distances, ed. by B. Müller, W. Greiner, G. Soff, J. Phys. B 12, L1 (1979)

    Google Scholar 

  68. See e.g. T.G. Heil, A. Dalgarno, Diabatic molecular states. J. Phys. B 12 L557 (1979) and references therein

    Google Scholar 

  69. G. Soff, V. Oberacker, W. Greiner, Inner-shell ionization induced by nuclear Coulomb excitation in collisions of very heavy-ions. Phys. Rev. Lett. 41, 1167 (1978)

    Article  ADS  Google Scholar 

  70. J. Reinhardt, V. Oberacker, B. Mller, G. Soff, W. Greiner, Positron emission in Pb-Pb and Pb-U collisions. Phys. Lett. B 78, 183 (1978) (with)

    Google Scholar 

  71. J. Reinhardt, B. Müller, W. Greiner, in Coherence and Correlation in Atomic Atomic Collisions, ed by. Kleinpoppen, Williams (Plenum Press, New York, 1980), p. 331

    Google Scholar 

  72. J. Reinhardt, W. Greiner, B. Müller, G. Soff in Electronic and Atomic Collisions, ed. by N. Oda, K. Takayanagi (North Holland, Amsterdam, 1980), p. 369

    Google Scholar 

  73. J. Reinhardt, U. Müller, B. Müller, W. Greiner, The decay of the vacuum in the field of superheavy nuclear systems. Z. Phys. A 303, 173 (1981)

    Article  ADS  Google Scholar 

  74. H. Backe et al., Observation of positron creation in superheavy-ion-atom collision systems. Phys. Rev. Lett. 40, 1443 (1978)

    Article  ADS  Google Scholar 

  75. C. Kozhuharov et al., Positrons from 1.4-GeV Uranium-atom collisions. Phys. Rev. Lett. 42, 376 (1979)

    Article  ADS  Google Scholar 

  76. J. Schweppe et al., EPOS Collaboration, Observation of a peak structure in positron spectra from U + Cm collisions. Phys. Rev. Lett. 51, 2261 (1983)

    Google Scholar 

  77. H. Backe et al., Estimates of the nuclear time delay in dissipative U + U and U + Cm collisions derived from the shape of positron and \(\delta \)-Ray spectra. Phys. Rev. Lett. 50, 1838 (1983)

    Article  ADS  Google Scholar 

  78. M. Clemente et al., Narrow positron lines from U-U and U-Th collisions. Phys. Lett. B 137, 41 (1984)

    Article  ADS  Google Scholar 

  79. W. Koenig et al., Positron lines from subcritical heavy-ion-atom collisions. Z. Phys. A 328, 129 (1987)

    ADS  Google Scholar 

  80. T. Cowan et al., EPOS Collaboration, Anomalous positron peaks from supercritical collisions systems. Phys. Rev. Lett. 54, 1761 (1985)

    Article  ADS  Google Scholar 

  81. T. Cowan et al., EPOS Collaboration, Observation of correlated narrow peak structures in positron and electron spectra from superheavy collision systems. Phys. Rev. Lett. 56, 444 (1986)

    Article  ADS  Google Scholar 

  82. P. Salabura et al., EPOS Collaboration “Correlated \(e^+e^-\) peaks observed in heavy-ion collisions,”. Phys. Lett. B 245, 153 (1990)

    Article  ADS  Google Scholar 

  83. H. Tsertos et al., Systematic studies of positron production in heavy-ion collisions near the Coulomb barrier. Z. Phys. A 342, 79 (1992)

    Google Scholar 

  84. I. Konig, E. Berdermann, F. Bosch, P. Kienle, W. Konig, C. Kozhuharov, A. Schroter, H. Tsertos, Investigations of correlated e+ e- emission in heavy-ion collisions near the Coulomb barrier. Z. Phys. A 346, 153 (1993)

    Article  ADS  Google Scholar 

  85. U. Leinberger et al., Orange at GSI Collaboration, New results on \(e^+e^-\) line emission in U+Ta collisions. Phys. Lett. B 394, 16 (1997)

    Google Scholar 

  86. I. Ahmad et al., APEX spectrometer experiment, Search for monoenergetic positron emission from heavy-ion collisions at Coulomb-Barrier energies. Phys. Rev. Lett. 78, 618 (1997)

    Google Scholar 

  87. I. Ahmad et al., APEX spectrometer experiment, Positron-electron pairs produced in heavy-ion collisions. Phys. Rev. C 60, 064601 (1999)

    Google Scholar 

  88. S. Heinz et al., ORANGE Collaboration, Positron spectra from internal pair conversion observed in U-238 + Ta-181 collisions. Eur. Phys. J. A 9, 55 (2000)

    Google Scholar 

  89. E. Widmann et al., Limits for two photon and e+ e- decay widths of positron—electron scattering resonances for \(\sqrt{s} = 1.78\) MeV to 1.92 MeV. Z. Phys. A 340, 209 (1991)

    Article  ADS  Google Scholar 

  90. B. Müller et al., Theoretical attempts to explain the GSI positron lines. AIP Conf. Proc. 189 479 (1989) Presented at: Relativistic, Quantum Electrodynamic and Weak Interaction Effects in Atoms (Santa Barbara, CA) 1 Jan–30 Jun 1988

    Google Scholar 

  91. S. Schramm, B. Müller, J. Reinhardt, W. Greiner, Decay of a composite particle as a hypothetical explanation of \(e^+ e^-\) coincidences observed at GSI. Mod. Phys. Lett. A 3, 783 (1988)

    Article  ADS  Google Scholar 

  92. J.R. Boyce, LIPSS and DarkLight and HPS and APEX Collaborations. J. Phys. Conf. Ser. 384, 012008 (2012). doi:10.1088/1742-6596/384/1/012008

  93. B.M. Hegelich, G.Mourou, J. Rafelski, Probing the quantum vacuum with ultra intense laser pulses. Eur. Phys. J. ST 223, 6 (2014), https://arxiv.org/abs/1412.8234

Download references

Author information

Authors and Affiliations

  1. Department of Physics, The University of Arizona, Tucson, AZ, 85721, USA

    Johann Rafelski

  2. Frankfurt Institute for Advanced Studies, Frankfurt, Germany

    Johannes Kirsch & Walter Greiner

  3. Department of Physics, Duke University, Durham, NC, 27708-0305, USA

    Berndt Müller

  4. Institut für Theoretische Physik, Goethe-Universität Frankfurt, Frankfurt, Germany

    Joachim Reinhardt

Authors
  1. Johann Rafelski
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Johannes Kirsch
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Berndt Müller
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Joachim Reinhardt
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Walter Greiner
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Johann Rafelski .

Editor information

Editors and Affiliations

  1. FIAS, Goethe University FIAS, Frankfurt, Hessen, Germany

    Stefan Schramm

  2. Frankfurt Inst. for Advanced Studies, FIAS Frankfurt Inst. for Advanced Studies, Frankfurt am Main, Germany

    Mirko Schäfer

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Rafelski, J., Kirsch, J., Müller, B., Reinhardt, J., Greiner, W. (2017). Probing QED Vacuum with Heavy Ions. In: Schramm, S., Schäfer, M. (eds) New Horizons in Fundamental Physics. FIAS Interdisciplinary Science Series. Springer, Cham. https://doi.org/10.1007/978-3-319-44165-8_17

Download citation

Publish with us

Policies and ethics

Search

Navigation