Hydrogen-like atom in a superstrong magnetic field: Photon emission and relativistic energy level shift

Nuclei, Particles, Fields, Gravitation, and Astrophysics
  • 21 Downloads

Abstract

Following our previous work, additional arguments are presented that in superstrong magnetic fields B ≫ (Zα)2B0, B0 = m2c3/ ≈ 4.41 × 1013 G, the Dirac equation and the Schrödinger equation for an electron in the nucleus field following from it become spatially one-dimensional with the only z coordinate along the magnetic field, “Dirac” spinors become two-component, while the 2 × 2 matrices operate in the {0; 3} subspace. Based on the obtained solution of the Dirac equation and the known solution of the “onedimensional” Schrödinger equation by ordinary QED methods extrapolated to the {0; 3} subspace, the probability of photon emission by a “one-dimensional” hydrogen-like atom is calculated, which, for example, for the Lyman-alpha line differs almost twice from the probability in the “three-dimensional” case. Similarly, despite the coincidence of nonrelativistic energy levels, the calculated relativistic corrections of the order of (Zα)4 substantially differ from corrections in the absence of a magnetic field. A conclusion is made that, by analyzing the hydrogen emission spectrum and emission spectra at all, we can judge in principle about the presence or absence of superstrong magnetic fields in the vicinity of magnetars (neutron stars and probably brown dwarfs). Possible prospects of applying the proposed method for calculations of multielectron atoms are pointed out and the possibility of a more reliable determination of the presence of superstrong magnetic fields in magnetars by this method is considered.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    V. V. Skobelev, J. Exp. Theor. Phys. 115, 76 (2012).ADSCrossRefGoogle Scholar
  2. 2.
    S. L. Adler, J. N. Bahcall, C. G. Callan, and M. N. Rosenbluth, Phys. Rev. Lett. 25, 1061 (1970).ADSCrossRefGoogle Scholar
  3. 3.
    V. V. Skobelev, J. Exp. Theor. Phys. 110, 211 (2010).ADSCrossRefGoogle Scholar
  4. 4.
    A. A. Sokolov, Introduction to Quantum Electrodynamics (Fizmatlit, Moscow, 1958).Google Scholar
  5. 5.
    V. B. Berestetskii, E. M. Lifshitz, and L. P. Pitaevskii, Course of Theoretical Physics, Vol. 4: Quantum Electrodynamics (Nauka, Moscow, 1989; Pergamon, Oxford, 1982).Google Scholar
  6. 6.
    V. V. Skobelev, J. Exp. Theor. Phys. 122, 248 (2016); Zh. Eksp. Teor. Fiz. 149, 909(E) (2016).ADSCrossRefGoogle Scholar
  7. 7.
    L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics, Vol. 3: Quantum Mechanics: Non-Relativistic Theory (Nauka, Moscow, 1974, 3th ed.; Pergamon, New York, 1977, 3rd ed.), rus. pp. 527, 150.Google Scholar
  8. 8.
    I. S. Gradshtein and I. M. Ryzhik, Tables of Integrals, Series and Products (Academic, New York, 2000; Fizmatgiz, Moscow, 1962).Google Scholar
  9. 9.
    A. A. Sokolov, Yu. M. Loskutov, and I. M. Ternov, Quantum Mechanics (Uchpedgiz, Moscow, 1962) [in Russian].MATHGoogle Scholar
  10. 10.
    G. Korn and T. Korn, Mathematical Handbook for Scientists and Engineers (Nauka, Moscow, 1968; McGraw-Hill, New York, 1961).MATHGoogle Scholar
  11. 11.
    G. Bethe and E. Salpeter, Quantum Mechanics of Oneand Two-Electron Atoms (Springer, Berlin, 1977; Nauka, Moscow, 1960).Google Scholar
  12. 12.
    V. V. Skobelev, Russ. Phys. J. 59, 48 (2016).CrossRefGoogle Scholar
  13. 13.
    V. V. Skobelev, Russ. Phys. J. 59, 1076 (2016).CrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Inc. 2017

Authors and Affiliations

  1. 1.Moscow Polytechnic UniversityMoscowRussia

Personalised recommendations