The Effect Of Thermal And Zero-Point Energy Of Quantum Vacuum On Spectra Of Finite-Sized Nucleus Of Hydrogen-Like Atoms

Authors

  • Aliyu Adamu Department of Physics, University of Maiduguri, P.M.B. 1069, Maiduguri, Nigeria Author
  • Usman A. Marte Department of Mathematical Sciences, University of Maiduguri, P.M.B. 1069, Maiduguri, Nigeria Author
  • Abdullahi U. U. Ocheni Department of Physics, University of Maiduguri, P.M.B. 1069, Maiduguri, Nigeria Author
  • Babagana Umaru Department of Basic Science Federal College of Freshwater Fisheries and technology, P. M. B. 1060, Baga, Nigeria Author
  • M. I. Bukar Department of Physics, University of Maiduguri, P.M.B. 1069, Maiduguri, Nigeria Author
  • Mamman Rawagana Department of Physics, University of Maiduguri, P.M.B. 1069, Maiduguri, Nigeria Author

DOI:

https://doi.org/10.60787/tnamp.v21.471

Keywords:

Vacuum Fields, Thermal Fluctuations, Quantum Electrodynamics, Energy Density, Zero-point Energy

Abstract

This study aims to accurately model the behavior of hydrogen-like and muonic atoms with finite-sized nuclei in quantum vacuum interactions, addressing the need for precise spectroscopy and accurate interpretation of experimental data across a wide temperature spectrum. The analysis uncovers that both the quantum number, n and nuclear charge, Z have a significant impact on the vacuum field and thermal effects. Muons, due to their greater mass and proximity to the nucleus, experience more pronounced thermal and vacuum field effects than electrons. The study’s findings emphasize the need to consider thermal contributions in quantum vacuum-related calculations and suggest that accounting for nuclear size differences can enhance the accuracy of muonic atom experiments. The study draws intriguing parallels between black holes and hydrogen atoms, offering exciting prospects for further exploration. The theoretical framework developed in this study holds promise for various scientific disciplines, opening new avenues for experimental investigations and deepening our understanding of fundamental physics. 

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References

Meis, C. (2020). Primary role of the quantum electromagnetic vacuum in gravitation and cosmology, IntechOpen. https://doi.org/10. 5772/intechopen.91157

Philip J. T. (2017). Zero-point energy and the emergence of gravity: Two hypotheses applied physicsresearch, Canadian Center of Science and Education, 9(2).

Planck, M. (1900). ZurTheorie des Gesetzes der EnergieverteilungimNormalspektrum. Verhandlungen der DeutschenPhysikalischenGesellschaft, 2(17), 237–245.

Planck, M. (1901). On the law of distribution of energy in the normal spectrum, Annalen der Physik, 4, 553-562. https://doi.org/10.1002/andp.19013090310

Kevin H. Knuth (2014, December). The Problem of motion: The statistical mechanics of Zitterbewegung. arXiv:1411.1854v2 [quant-ph].

Maclay G. J. (2020). History and some aspects of the lamb shift, Physics, 2, 105–149. https://doi.org/10.3390/physics2020008

The Role of Vacuum Fluctuations and Symmetry in the Hydrogen Atom in Quantum Mechanics and Stochastic Electrodynamics, Atoms. 2019; 7(39).

Clóves, G. R., Antônio, A. P. S., Carlos, A. B. S., Áurea, R. V., Galvão Ramos, J., & Roberto, L. (2010). The role of nonequilibrium thermo-mechanical statistics in modern technologies and industrial processes: An overview. Brazilian Journal of Physics, 40 (1). https://doi.org/10.1590/S0103-97332010000100011

Einstein, A. (1917). Cosmological considerations in the general theory of relativity. Sitzungsber. Preuss. Akad. Wiss, Berlin (Math.Phys.), 142–152.

Pasquale, C. & John, C. (2006). Entanglement entropy and quantum field theory: A non-technical introduction. International Journal of Quantum Information 4, 429. https://doi.org/10.48550/arXiv.quant-ph/0505193

Faria, A. J., Franca, H. M., Gomes, G. G., &Sponchiado, R. C. (2006). The vacuum electromagnetic fields and the Schrodinger picture, arXiv:quant-ph/0510134v2.

Borie, E. (2012). Lamb shift in light muonic atoms — Revisited. Annals of Physics, 327, 733–763.

Marshall, T. W. (1963). Random electrodynamics. In Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 276 (1368), 475–491.

Boyer, T. H. (1975). General connection between random electrodynamics and quantum electrodynamics for free electromagnetic fields and for dipole oscillator systems. Physical Review D, 11(4), 790–808.

Milonnni, P. W. (1984). Why spontaneous emission? American Journal of Physics, 52 (4), 340–343.

Eisberg, R. (1985). Quantum physics of atoms, molecules, solids, nuclei, and particles. 2nd Edition. John Wiley &Sons, New York.

Griffiths, D. J. (1995). Introduction to quantum mechanics, Prentice Hall, Inc., New Jersey, USA.

David, H. (1990). The Zitterbewegung interpretation of quantum mechanics. Foundation of Physics. 20 (10), 1213–1232.

Olszewski, S. (2014). De Broglie’s velocity of transition between quantum levels and the quantum of the magnetic spin moment obtained from the uncertainty principle for energy and time. Journal of Modern Physics, 5, 2022-2029. http://dx.doi.org/10.4236/jmp.2014.518198.

Adonai S. S. A., & Daniel, C. F. (n.d.). The temperature of the quantum vacuum. Department of Mathematics, Federal University at Parana P.O. Box 19081, Curitiba, PR, 81531-990, Brazil.

De la Peña, L., Valdés-Hernández, A., &Cetto, A. M. (2008). Statistical consequences of the zero-point energy of the harmonic oscillator, Am. J. Phys., 76, 947–955.

Boyer, T. H. (2003). Conjectured derivation of the Planck radiation spectrum from Casimir energies, J. Phys. A Math. Gen., 36, 7425–7440.

Dalibard, J., Dupont-Roc, J., & Cohen-Tannoudji, C. (1982). Vacuum fluctuations and radiation reaction: Identification of their respective contributions,Journal Physique, 43(11), 1617–1638.

Moddel, G., &Dmitriyeva, O. (2019). Extraction of zero-point energy from the vacuum: Assessment of Stochastic electrodynamics-based approach as compared to other methods, atoms, 7(51). https://doi.org/10.3390/atoms7020051

Michaud, A. (2017). Gravitation, quantum mechanics and the least action electromagnetic equilibrium states, Journal of Astrophysics & Aerospace Technology, 5(2), 1000152. https://doi.org/10.4172/2329-6542.1000152

Genet, C., Intravaia, F., Lambrecht, A., & Reynaud, S. (2004). Electromagnetic vacuum fluctuations, Casimir and Van der Waals forces. Annales de la Fondation Louis de Broglie, 29(1–2), 331–348.

Walcher, T. (2023). The lamb shift in muonic hydrogen and the electric rms radius of the proton. arXiv:2304.07035v1 [physics.atom-ph].

Vaks, V. G. (1959). Radiative deviations from the Coulomb law at small distances, Soviet Physics JETP, 36 (9), 1340–1344.

Reynand, S., Lambrecht, A., Genet, C., &Jaekel, M. T. (2001). Quantum vacuum fluctuations, arXiv:quant-ph/0105053v2. https://doi.org/10.48550/ arXiv.quant-ph/0105053

Oppenheimer, J. R. (1930). Note on the theory of the interaction of field and matter. Physical Review, 35(5), 461–477. https://doi.org/10.113/phyRev.35.461

Bethe, H. A. (1947). The electromagnetic shift of energy levels. Physical Review, 72, 339–341.

Lamb Jr., W. E. &Retherford, R. C. (1947). Fine structure of the hydrogen atom by a microwave method, Physical Review, 72 (3), 241.

Sidharth, B. G., & Das, A. (2017). The Zitterbewegung region, International Journal of Modern Physics A, 32, 19–20.

Peskin, M. E. & Schroeder, D. V. (2018). An introduction to quantum field theory, CRC Press, Taylor & Francis Group.

Feynman, R. P. (1948). Space-time approach to non-relativistic quantum mechanics. Reviews of Modern Physics, 20(2), 367–387. https://doi.org/10.1103/RevModPhys.20.367.

Mandl, F., & Shaw, G. (2010). Quantum field theory, 2nd Edition. John Wiley & Sons.

Greiner, W., & Reinhardt, J. (2009). Field quantization, Springer Science & Business Media.

LeBlanc, J., Beeler, J. M. C., Jimenez-Garcia, K., Perry, A. R., Sugawa, S., Williams, R. A. &Spielman, I. B. (2013). Direct observation of Zitterbewegung in a Bose-Einstein condensate. New Journal of Physics, 15 (073011), 1–11.

Tangherlini, F. R. (2022). Highly accurate relations between the fine structure constant and particle masses, with application to its cosmological measurement, Journal of Modern Physics, 13, 682–699. https://doi.org/10.4236/jmp.2022.135038.

Adamu, A., Hassan, M., Dikwa, M. K. &Amshi, S. A. (2018). Determination of nuclear structure effects on atomic spectra by applying Rayleigh–Schrödinger perturbation theory. AmericanJournal of Quantum Chemistry and Molecular Spectroscopy, 2(2), 39–51.

Adamu, A. &Ngadda, Y. H. (2015). The nuclear finite–size corrections to energies of n = 1, n = 2 and n = 3 states of hydrogen atom.Journal of the Nigerian Association of Mathematical Physics, 30, 137–137.

Pardy, M. (2016). Energy Shift of H-Atom Electrons Due to Gibbons-Hawking Thermal Bath. Journal of High Energy Physics, Gravitation and Cosmology, 2, 472–477.

Michel, N., &Oreshkina, N. S. (2021). Access to the Kaon radius with Kaonic atoms. Annalen der Physik (Berlin), 2100150. https://doi.org/10.1002/andp.202100150

Oreshkina, N. S. (2022). Self-energy correction to the energy levels of heavy muonic atoms, arXiv:2206.01006v1 [physics.atom-ph]. https://doi.org/10.48550/arXiv.2206.01006

Shahaev V. M. (1993). Finite nuclear size corrections to the energy levels of the multicharged ions,Journal of Physics B: Atomic Molecular and Optical Physics, 26, 1103–1108. Printed in the UK.

Kumar A., Das, H. C., Kaur, M., Bhuyan, M., & Patra, S. K. (2021). Nuclear matter parameters for finite nuclei using relativistic mean field formalism within coherent density fluctuation model, Physical Review C, 103: 024305.

Niri, B. N. &Anjami, A. (2018). Nuclear size corrections to the energy levels of single-electron atoms, Nuclear Science, 3(1), 1–8.

Deck, R. T., Amar, J. G. &Fralick, G. (2005). Nuclear size corrections to the energy levels of single-electron and -muon atoms, Journal of Physics B: Atomic Molecular and Optical Physics, 38, 2173–2186.

Neznamov, V. P. &Safronov, I. I. (2014). A new method for solving the Z > 137 problem and for determination of energy levels of hydrogen-like atoms, World Scientific, 100, 167–180.

Blatt, J. M. (2006). Practical points concerning the solution of the Schrödinger equation. Journal of Computational Physics, 1(3), 382-396. https://doi.org/10.1016/0021-9991(67)90046-0

Evans M. W. &Eckardt, H. (2011). The lamb shift in atomic hydrogen calculated from Einstein–Cartan–Evans (ECE) field theory, Journal of Foundations of Physics and Chemistry, 1(5), 493–520.

Venkataram, P. S. (2013). Electromagnetic field quantization and applications to the Casimir effect. MIT Department of Physics: 8.06. (Dated: May 6, 2013).

Moddel, G. &Dmitriyeva, O. (2019). Extraction of zero-point energy from the vacuum: Assessment of Stochastic electrodynamics-based approach as compared to other methods, Atoms, 7(51) https://.

Dyson, F. J. (2006). Advanced quantum mechanics, 2nd Edition arXiv:quant-ph/0608140v1 18 Aug 2006, page 50 – 51.

Oyendande, O. E. (2022). Quantum Mechanics. Leaf Light Books Ltd., Nigeria. Page 4.

Marshall, L. B. (2012). Modern physics for science and engineering. Physics Curriculum & Instruction, Inc. Produced in the United States of America.

Valone, T. (2005). Feasibility study of zero-point energy extraction from the quantum vacuum for the performance of useful work, 3rd Edition, Integrity Research Institute, https://doi.org/10.13140/2.1.3117.3129.

Adamu A., (2016). Corrections to the energy levels of finite – size nuclei due to fluctuating electromagnetic fields in vacuum. Journal of the Nigerian Association of Mathematical Physics, 36, 215–222.

Adamu, A., Ngadda, Y. H., Hassan, M. & Malgwi, D. I. (2020). The Coulomb energy of finite size nucleus from the study of classical electrodynamics theory. NIPES Journal of Science and Technology Research, 2(3), 272–282.

Greiner, W. (2001). Quantum mechanics: An introduction 4th Edition Springer, Berlin, Germany, page 181, 220–227.

Gasiorowicz, S. (2003). Quantum physics 3rd Edition John Wiley & Sons, Inc., the United States of America.

Das, A. &Sidharth, B. G. (2015). Revisiting the Lamb Shift. European Journal of Theoretical Physics, 12 (IYL15-34), 139–152.

House, J. E. (2018). Fundamentals of Quantum Mechanics: 3rd Edition. Academic Press is an imprint of Elsevier, United Kingdom, page 63.

Schwab, F. (2005). Advanced quantum mechanics. Springer-Verlag Berlin, page 41–52.

El Shabshiry, M., Ismaeel, S. M. E. & Abdel-Mageed, M. M., (2015). Finite size uehling corrections in energy levels of hydrogen and muonic hydrogen atom. IOSR Journal of Applied Physics, 7(5), 60– 66.

Welton, Th. (1948). Some observable effects of the quantum-mechanical fluctuations of the electromagnetic field. Physical Review, Vol. 74, Pp 1157.

Weisskopf, V. F. (1949). Recent development in the theory of the electron, Review of Modern Physics, 21(2), 305 – 315.

Adamu, A., Ngadda, Y. H. & Hassan, M. (2019). The effect of vacuum fields fluctuation on orbiting electron. Nigerian Institute of Physics, 27(1), 184–190.

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Published

2025-03-03

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The Effect Of Thermal And Zero-Point Energy Of Quantum Vacuum On Spectra Of Finite-Sized Nucleus Of Hydrogen-Like Atoms. (2025). The Transactions of the Nigerian Association of Mathematical Physics, 21, 27-43. https://doi.org/10.60787/tnamp.v21.471

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