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Relativistic decay rates of one-electron atoms

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Abstract

The literature contains several analytic or semianalytic formulas that can be used to calculate various decay rates of the relativistic hydrogenic atom. To date, all of these formulas depend on two-component atomic wavefunctions. In this paper we derive the necessary working formulas needed to evaluate the decay rate for M1, E1, E2 or M2 transitions with a four-component wavefunction. We also show that both methods yield identical results.

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References

  1. A. Kolakowska, J. Phys. B 29, 4515 (1996)

    Article  CAS  Google Scholar 

  2. J. Dolbeault, M.J. Esteban, E. Séré, M. Vanbreugel, Phys. Rev. Lett. 85, 4020 (2000)

    Article  CAS  Google Scholar 

  3. R.P. Martinez-y-Romero, Am. J. Phys. 68, 1050 (2000)

    Article  CAS  Google Scholar 

  4. A.L.A. Fonseca, D.L. Nascimento, F.F. Monteiro, M.A. Amato, J. Mod. Phys. 3, 350 (2012)

    Article  Google Scholar 

  5. B.K. Datta, N. Rahman, R.C. Bhowmik, S. Paul, M.R. Kabir, U. Roy, Int. J. Sci. Eng. Tech. 3, 342 (2014)

    Google Scholar 

  6. I.A. Assi, H. Bahlouli, J. Appl. Math. Phys. 5, 2072 (2017)

    Article  Google Scholar 

  7. S.N. Datta, Indian J. Phys 93, 285 (2019)

    Article  CAS  Google Scholar 

  8. G. Aissing, Phys. Rev. A 44, R2765 (1991)

    Article  CAS  Google Scholar 

  9. J. Seke, Mod. Phys. Lett. B 9, 1771 (1995)

    Article  CAS  Google Scholar 

  10. J. Seke, Physica A 233, 469 (1996)

    Article  CAS  Google Scholar 

  11. A.V. Soldatov, J. Seke, G. Adam, Int. J. Mod. Phys. B 22, 3825 (2007)

    Article  Google Scholar 

  12. A.V. Soldatov, J. Seke, G. Adam, M. Polak, Mod. Phys. Lett. B 23, 111 (2009)

    Article  CAS  Google Scholar 

  13. V.G. Pal’chikov, Phys. Scr. 57, 581 (1998)

    Article  Google Scholar 

  14. B.A. Robson, S.H. Sutanto, Int. J. Theor. Phys. 40, 1475 (2001)

    Article  CAS  Google Scholar 

  15. O. Jitrik, C.F. Bunge, J. Phys. Chem. Ref. Data 33, 1059 (2004)

    Article  CAS  Google Scholar 

  16. O. Jitrik, C.F. Bunge, Phys. Scr. 69, 196 (2004)

    Article  CAS  Google Scholar 

  17. L. Morel, Z. Yao, P. Cladé, S. Guellati-Khélifa, Nature 588, 61 (2020)

    Article  CAS  Google Scholar 

  18. T.P. Das, Relativistic Quantum Mechanics of Electrons (Harper and Row, New York, 1973)

    Google Scholar 

  19. J.J. Sakurai, Advanced Quantum Mechanics (Addison-Wesley, New York, 1967)

    Google Scholar 

  20. H.A. Bethe, Intermediate Quantum Mechanics (W.A. Benjamin, New York, 1964)

    Google Scholar 

  21. I.P. Grant, Relativistic Quantum Theory of Atoms and Molecules: Theory and Computation (Springer, New York, 2007)

    Book  Google Scholar 

  22. I.P. Grant, J. Phys. B 7, 1458 (1974)

    Article  CAS  Google Scholar 

  23. M. Mizushima, Quantum Mechanics of Atomic Spectra and Atomic Structure (W.A. Benjamin, New York, 1970)

    Google Scholar 

  24. K. Balasubramanian, Relativistic Effects in Chemistry: Theory and Techniques and Relativistic Effects in Chemistry (John Wiley & Sons, New York, 1997)

    Google Scholar 

  25. F.A. Parpia, A.K. Mohanty, Phys. Rev. A 52, 962 (1995)

    Article  CAS  Google Scholar 

  26. H.M. Quiney, H. Skaane, I.P. Grant, Advances in Quantum Chemistry, vol. 32, ed. by Per-Olov Lowdin et al., (Academic Press, New York, 1998)

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Acknowledgements

We want to thank Drs. Silvia Sutanto and Brian Robson for several generous communications that helped us understand their work. Our deepest appreciation goes to Professor Ian Grant for graciously answering innumerable questions about relativistic decay rates.

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Authors and Affiliations

  1. Department of Physics, Southwestern University, Georgetown, TX, 78626, USA

    Gerardo Gonzalez & S. A. Alexander

  2. Department of Physics, University of Florida, Gainesville, FL, 32611, USA

    R. L. Coldwell

Authors
  1. Gerardo Gonzalez
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  2. S. A. Alexander
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  3. R. L. Coldwell
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Correspondence to S. A. Alexander.

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Gonzalez, G., Alexander, S.A. & Coldwell, R.L. Relativistic decay rates of one-electron atoms. J Math Chem 61, 193–218 (2023). https://doi.org/10.1007/s10910-022-01406-y

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  • DOI: https://doi.org/10.1007/s10910-022-01406-y

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