Estimation of Relativistic Mass Correction for Electronic and Muonic Hydrogen Atoms with Potential from Finite Size Source
The simplest atom known to exist in nature is electronic hydrogen atom, which helps us to study fundamental properties and structure of atoms. We can also have muonic hydrogen by replacing electron with muon. In this paper, we revisit Schrodinger equation as an attempt to address the relativistic mass correction to electronic and muonic hydrogen-like atoms with potentials from finite size sources. This study is done with the assumption that the changes in both energy eigenvalues and eigenfunctions are negligible when considering the finite size of the nuclei. The relativistic mass corrections to and states using potential from finite size source are obtained and compared with corrections using potential from point-like source. The results show that, for hydrogen-like atoms with light nuclei the relativistic mass corrections due to the finite size source roughly coincides with that of point-like source. However, for atoms with heavy nuclei the two corrections display strong disagreement in which the corrections with finite size nuclei are significantly smaller than that of point-like nuclei.
 Hudson, A., Nelson, R. 1990. University physics Volume Two, 2nd edition.
 Beiser, A. 2003. Concepts of Modern Physics. 6th edition. McGraw-Hill, New York.
 Pohl, R. Gilman, R., Miller, G. A., Pachucki. 2013. Muonic Hydrogen and the Proton Radius Puzzle. Annual Review of Nuclear and Particle Science, 63 (1).
 Pohl, R. 2014. The Lamb shift in muonic hydrogen and the proton radius puzzle. Hyperfine Interactions, 227 (1-3): 23-28.
 Kena, E. D., & Adera, G. B. 2021. Solving the Dirac equation in central potential for muonic hydrogen atom with point-like nucleus. Journal of Physics Communications, 5(10), 105018.
 Firew, M. 2020. Investigating Muonic Hydrogen Atom Energy Spectrum Using
Perturbation Theory in Lowest Order. Adv. Phys. App. 83.
 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(13): 2173—2186.
 Schwabl, F. 2008. Advanced Quantum Mechanics 4th edition, Springer-Verlag Berlin Heidelberg.
 Townsend, J.S. 2012. A modem approach to quantum mechanics, 2nd edition.
 Maggiore, M. 2005. A Modern Introduction to Quantum Field Theory. Oxford University Press.
 Messiah A. 1966 Quantum Mechanics Volume II (New York: John Wiley and sons Inc.)
 Griffiths, J. D., 1995. Introduction to Quantum mechanics 2nd edition, Prentice Hall, Inc., New Jersey, USA.
 Sakurai, J.J. and Napolitano, J. 2011. Modern Quantum Mechanics 2nd edition, Addison-Wesley
 Krane, K.S. 1988. Introductory Nuclear Physics. John Wiley & Sons. New York.
 Arfken, G. B. and Weber, H. J. 2005. Mathematical Methods for Physicists 6th Edition, Elsevier Inc.
 IAEA Nuclear Data Services. https://www-nds.iaea.org/radii/
Copyright (c) 2022 Ethiopian Journal of Sciences and Sustainable Development
This work is licensed under a Creative Commons Attribution 4.0 International License.