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About the hydrogenoid atoms in the timeless three-dimensional quantum vacuum

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Abstract

A new understanding of the hydrogenoid atoms, both in the non-relativistic domain and for the relativistic Dirac electron, as well as regarding the phenomenon of the Lamb shift, is provided in a model based on energy fluctuations of a timeless three-dimensional quantum vacuum corresponding to elementary processes of creation/annihilation of quanta.

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References

  1. Bohr, N.: On the constitution of atoms and molecules, part I. Philos. Mag. 26, 1 (1913)

    Article  MATH  Google Scholar 

  2. Heisenberg, W.: Uber quantentheoretische Umdeutung kinematischer und mechanischer Beziehungen. Z. Phys. 33, 879 (1925)

    Article  MATH  Google Scholar 

  3. Born, M., Jordan, P.: Zur Quantenmechanik. Z. Phys. 34, 858 (1925)

    Article  MATH  Google Scholar 

  4. Born, M., Heisenberg, W., Jordan, P.: Zur Quantenmechanik. II. Z. Phys. 35, 557 (1926)

    Article  MATH  Google Scholar 

  5. Pauli, W.: Uber das Wasserstoffspektrum vom Standpunkt der neuen Quantenmechanik. Z. Phys. 36, 336 (1926)

    Article  MATH  Google Scholar 

  6. Pauli, W.: Zur Quantenmechanik des magnetischen Elektrons. Z. Phys. 43, 601 (1927)

    Article  MATH  Google Scholar 

  7. Schrödinger, E.: Quantisierung als Eigenwertproblem. Ann. Phys. 384, 361 (1926)

    Article  MATH  Google Scholar 

  8. Dirac, P.A.M.: The quantum theory of the electron. Proc. R. Soc. A 117, 610 (1928)

    Article  MATH  Google Scholar 

  9. Dirac, P.A.M.: The quantum theory of the electron. Part II. Proc. R. Soc. A 118, 351 (1928)

    Article  MATH  Google Scholar 

  10. Gordon, W.: Die Energieniveaus des Wasserstoffatoms nach der Diracschen Quantentheorie des Elektrons. Z. Phys. 48, 11 (1928)

    Article  MATH  Google Scholar 

  11. Michelson, A.A.: Application of interference methods to spectroscopic measurement. Publ. Astron. Soc. Pac. 4, 190 (1892)

    Article  Google Scholar 

  12. Lamb, Tr W.E., Retherford, R.C.: Fine structure of the hydrogen atom by a microwave method. Phys. Rev. 72, 241 (1947)

    Article  Google Scholar 

  13. Bethe, H.A.: The electromagnetic shift of energy levels. Phys. Rev. 72, 339 (1947)

    Article  MATH  Google Scholar 

  14. Mohr, P.J.: Self-energy radiative corrections in hydrogen-like systems. Ann. Phys. (NY) 88(1), 26–51 (1974)

    Article  Google Scholar 

  15. Mohr, P.J.: Numerical evaluation of the 1S12-state radiative level shift. Ann. Phys. (NY) 88(1), 52–87 (1974)

    Article  Google Scholar 

  16. Mohr, P.J.: Self-energy of the \(\text{ n } = 2\) states in a strong Coulomb field. Phys. Rev. A 26, 2338 (1982)

    Article  Google Scholar 

  17. Mohr, P.J.: Energy levels of hydrogen-like atoms predicted by quantum electrodynamics, \(10 \le \text{ Z } \le 40\). At. Data Nucl. Data Tables 29, 453–466 (1983)

    Article  Google Scholar 

  18. Johnson, W.R., Soff, G.: The lamb shift in hydrogen-like atoms, \(1 \le \text{ Z } \le 110\). At. Data Nucl. Data Tables 33(3), 405–446 (1985)

    Article  Google Scholar 

  19. Soff, G., Mohr, P.J.: Vacuum polarization in a strong external field. Phys. Rev. A 38(10), 5066–5075 (1988)

    Article  Google Scholar 

  20. Manakov, N.L., Nekipelov, A.A., Fainshtein, A.G.: Vacuum polarization by a strong coulomb field and its contribution to the spectra of multiply-charged ions. Zh. Eksp. Teor. Fiz. 95, 1167–1177 (1989). [Sov. Phys. JETP 68, 673 (1989)]

    Google Scholar 

  21. Mohr, P.J., Soff, G.: Nuclear size correction to the electron self-energy. Phys. Rev. Lett. 70(2), 158–161 (1993)

    Article  Google Scholar 

  22. Artemyev, A.N., Shabaev, V.M., Yerokhin, V.A.: Relativistic nuclear recoil corrections to the energy levels of hydrogenlike and high-Z lithiumlike atoms in all orders in alpha Z. Phys. Rev. A 52(3), 1884–1894 (1995)

    Article  Google Scholar 

  23. Plunien, G., Soff, G.: Nuclear-polarization contribution to the Lamb shift in actinide nuclei. Phys. Rev. A 51, 1119 (1995) [(Erratum) Phys. Rev. A 53, 4614 (1996)]

  24. Yerokhin, V.A., Shabaev, V.M.: Two-loop self-energy correction in H-like ions. Phys. Rev. A 64, 062507 (2001)

    Article  Google Scholar 

  25. Yerokhin, V.A., Indelicato, P., Shabaev, V.M.: Two-loop self-energy correction in high-Z hydrogenlike ions. Phys. Rev. Lett. 91, 073001 (2003)

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

  27. Wichmann, E.H., Kroll, N.M.: Vacuum polarization in a strong Coulomb field. Phys. Rev. A 101, 843–859 (1956)

    Article  MathSciNet  MATH  Google Scholar 

  28. Persson, H., Lindgren, I., Salomonson, S., Sunnergren, P.: Accurate vacuum-polarization calculations. Phys. Rev. A 48(4), 2772–2778 (1993)

    Article  Google Scholar 

  29. Sapirstein, J., Cheng, K.T.: Vacuum polarization calculations for hydrogenlike and alkali-metal-like ions. Phys. Rev. A 68, 042111 (2003)

    Article  Google Scholar 

  30. Yerokhin, V.A.: Nuclear-size correction to the Lamb Shift of one-electron atoms. Phys. Rev. A 83, 012507 (2011)

    Article  Google Scholar 

  31. Manakov, N.L., Nekipelov, A.A.: Vestnik VGU 2, 53; [in Russian, http://www.vestnik.vsu.ru/pdf/physmath/2012/02/2012-02-07.pdf] (2012)

  32. Manakov, N.L., Nekipelov, A.A.: Vestnik VGU 2, 84; [in Russian, http://www.vestnik.vsu.ru/pdf/physmath/2013/02/2013-02-08.pdf] (2013)

  33. Yerokhin, V.A., Shabaev, V.M.: Lamb shift of \(\text{ n } = 1\) and \(\text{ n } = 2\) states of hydrogenlike atoms, \(1\le Z\le 110\). arXiv:1506.01885v1 [physics.atom-ph] (2015)

  34. Bu, S-L.: Negative energy: from lamb shift to entanglement. arXiv:1605.08268v1 [physics.gen-ph] (2016)

  35. Fiscaletti, D., Sorli, A.: Perspectives about quantum mechanics in a model of a three-dimensional quantum vacuum where time is a mathematical dimension. SOP Trans. Theor. Phys. 1(3), 11–38 (2014)

    Article  Google Scholar 

  36. Fiscaletti, D., Sorli, A.: Space-time curvature of general relativity and energy density of a three-dimensional quantum vacuum. Ann. UMCS Sectio AAA Phys. LXV, 53–78 (2014)

  37. Fiscaletti, D., Sorli, A.: About a three-dimensional quantum vacuum as the ultimate origin of gravity, electromagnetic field, dark energy... and quantum behaviour. Ukr. J. Phys. 61(5), 413–431 (2016)

    Article  Google Scholar 

  38. Fiscaletti, D., Sorli, A.: Dynamic quantum vacuum and relativity. Ann. UMCS Sectio AAA Phys. LXXI, 11–52 (2016)

  39. Fiscaletti, D., Sorli, A.: Quantum relativity: variable energy density of quantum vacuum as the origin of mass, gravity and the quantum behaviour. Ukr. J. Phys. 63(7), 623–644 (2018)

    Article  Google Scholar 

  40. Dirac, P.A.M.: Principles of Quantum Mechanics, 4th edn. Oxford University Press, Oxford (1982)

    Google Scholar 

  41. Erickson, G.W.: Improved Lamb-shift calculation for all values of Z. Phys. Rev. Lett. 27, 780–783 (1971)

    Article  Google Scholar 

  42. Bettini, A.: Introduction to Elementary Particle Physics. Cambridge University Press, Cambridge (2008)

    Book  Google Scholar 

  43. Rubakov, V.A.: Hierarchies of fundamental constants. Phys. Uspekhi Adv. Phys. Sci. 50(4), 390–396 (2007)

    Article  Google Scholar 

  44. Carroll, S.M., Press, W.H., Turner, E.L.: The cosmological constant. Ann. Rev. Astron. Astrophys. 30(1), 499–542 (1992)

    Article  MathSciNet  Google Scholar 

  45. Chernin, A.D.: Dark energy and universal antigravitation. Phys. Uspekhi Adv. Phys. Sci. 51(3), 253–282 (2008)

    Article  Google Scholar 

  46. Padmanabhan, T.: Darker side of the Universe, \(29^{\circ }\). Int. Cosmic Ray Conf. Pune 10, 47–62 (2005)

    Google Scholar 

  47. Reichhardt, T.: Cosmologists look forward to clear picture. Nature 421, 777 (2003)

    Article  Google Scholar 

  48. Sahni, V.: “Dark matter and dark energy”, Lecture Notes in Physics 653, 141–180 (2004). e-print: arXiv:astro-ph/0403324

  49. Zeldovich, YuB: Vacuum theory: a possible solution to the singularity problem of cosmology. Phys. Uspekhi Adv. Phys. Sci. 24(3), 216–230 (1981)

    Google Scholar 

  50. Snyder, H.S.: Quantized space-time. Phys. Rev. 71(1), 38–41 (1947)

    Article  MathSciNet  MATH  Google Scholar 

  51. Bojowald, M., Kempf, A.: Generalized uncertainty principles and localization of a particle in discrete space. Phys. Rev. D 86, 085017 (2012)

    Article  Google Scholar 

  52. Gao, S.: Why gravity is fundamental. arXiv:1001.3029 (2010)

  53. Ng, Y.J.: Holographic foam, dark energy and infinite statistics. Phys. Lett. B 657(1), 10–14 (2007)

    Article  Google Scholar 

  54. Ng, Y.J.: Spacetime foam: from entropy and holography to infinite statistics and non-locality. Entropy 10(4), 441–461 (2008)

    Article  MathSciNet  Google Scholar 

  55. Ng, Y.J.: Holographic quantum foam. arXiv:1001.0411v1 [gr-qc] (2010)

  56. Ng, Y.J.: Various facets of spacetime foam. arXiv:1102.4109.v1 [gr-qc] (2011)

  57. Chiatti, L.: The transaction as a quantum concept. In: Licata, I. (ed.) Space-time geometry and quantum events, pp. 11–44, Nova Science Publishers, New York (2014). e-print arXiv:1204.6636 (2012)

  58. Licata, I.: Transaction and non-locality in quantum field theory. In: European Physical Journal Web of Conferences (2013)

  59. Licata, I., Chiatti, L.: Timeless approach to quantum jumps. Quanta 4(1), 10–26 (2015)

    Article  Google Scholar 

  60. Licata, I., Chiatti, L.: Archaic universe and cosmological model: ’big-bang’ as nucleation by vacuum. Int. J. Theor. Phys. 49(10), 2379–2402 (2010)

  61. Fiscaletti, D., Sorli, A., Klinar, D.: The symmetrized quantum potential and space as a direct information medium. Annales de la Fondation Loius de Broglie 37, 41–71 (2012)

    MathSciNet  MATH  Google Scholar 

  62. Ballentine, L.E.: Quantum Mechanics. Prentice Hall, Upper Saddle River (1990)

    MATH  Google Scholar 

  63. Licata, I., Fiscaletti, D.: Bell length as mutual information in quantum interference. Axioms 3, 153–165 (2014)

    Article  MATH  Google Scholar 

  64. Fiscaletti, D., Licata, I.: Bell length in the entanglement geometry. Int. J. Theor. Phys. 54(7), 2362–2381 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  65. Chiatti, L., Licata, I.: Fluidodynamical representation and quantum jumps. In: Kastner, R.E., Jeknic-Duzic, J. (eds.) Quantum structural studies, pp. 201–224. World Scientific, Singapore (2017)

  66. Fiscaletti, D., Sorli, A.: Quantum vacuum energy density and unifying perspectives between gravity and quantum behaviour of matter. Annales de la Fondation Louis de Broglie 42(2), 251–297 (2017)

    MathSciNet  Google Scholar 

  67. Hernandez-Zapata, S.: The Dirac equation from a bohmian point of view. arXiv:1003.1558 [quant-ph] (2010)

  68. Chavoya-Aceves, O.: A de Broglie–Bohm like model for Dirac equation. arXiv:quant-ph/0304195 (2003)

  69. Bjorken, J.D., Drell, S.D.: Relativistic Quantum Mechanics. McGraw-Hill, New York (1964)

    MATH  Google Scholar 

  70. Hiley, B.J.: Is the electron stationary in the ground state of the Dirac hydrogen atom in Bohm’s theory. arXiv:1412.5887v1 [quant-ph] (2014)

  71. Sbitnev, V.: Navier–Stokes equation describes the movement of a special superfluid medium. arXiv:1504.07497v1 [quant-ph] (2015)

  72. Sbitnev, V.: Physical vacuum is a special superfluid medium. In: Pahlavani, M.R. (ed.) Selected Topics in Applications of Quantum Mechanics, pp. 345–373. InTech, Rijeka (2015)

    Google Scholar 

  73. Sbitnev, V.: Hydrodynamics of the physical vacuum: dark matter is an illusion. Mod. Phys. Lett. A 30(35), 1550184 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  74. Sbitnev, V.: Hydrodynamics of the physical vacuum. I: scalar quantum sector. Found. Phys. 46, 5, 606–619 (2016). e-print arXiv:1504.07497.v2 [quant-ph] (2016)

  75. Volovik, G.E.: The Universe in a Helium Droplet. Clarendon Press, Oxford (2003)

    MATH  Google Scholar 

  76. Welton, T.A.: Some observable effects of the quantum mechanical fluctuations of the electromagnetic field. Phys. Rev. 74, 1157 (1948)

    Article  MATH  Google Scholar 

  77. Weisskopf, V.F.: Recent developments in the theory of the electron. Rev. Mod. Phys. 21, 305 (1949)

    Article  MATH  Google Scholar 

  78. Das, A., Sidhart, B.G.: Revisiting the Lamb-shift. Electron. J. Theor. Phys. 12(IYL15–34), 139–152 (2015)

    Google Scholar 

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Fiscaletti, D., Sorli, A. About the hydrogenoid atoms in the timeless three-dimensional quantum vacuum. Quantum Stud.: Math. Found. 6, 431–451 (2019). https://doi.org/10.1007/s40509-019-00184-8

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