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Determination of Nuclear Structure Effects on Atomic Spectra by Applying Rayleigh–Schrödinger Perturbation Theory

American Journal of Quantum Chemistry and Molecular Spectroscopy

Volume 2, Issue 2, December 2018, Pages: 39-51

Received: Aug. 29, 2018; Accepted: Sep. 11, 2018; Published: Jan. 11, 2019

Volume 2, Issue 2, December 2018, Pages: 39-51

Received: Aug. 29, 2018; Accepted: Sep. 11, 2018; Published: Jan. 11, 2019

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Authors

Aliyu Adamu, Department of Physics, University of Maiduguri, Borno, Nigeria

Muhammad Hassan, Department of Physics, University of Maiduguri, Borno, Nigeria

Mohammed Kyari Dikwa, Department of Physical Science, School of Health Technology Maiduguri, Borno, Nigeria

Salamatu Ahmad Amshi, Department of Pharmaceutical Chemistry, University of Maiduguri, Borno, Nigeria

Abstract

In this work, we applied the first order time independent Rayleigh–Schrödinger Perturbation Theory, as an approximation method to calculate numerically the corrections in atomic spectra due to nuclear structure effects. The results showed that the nuclear structure effects distort the atomic spectra in different ways: The combined fine structure effect which decreases with increasing values of *n*, split the quantum number *n* into *l±*½ and the magnitude of the energy levels shift is of order of 10^{-6} *eV* relative to the energy levels calculated from the non-relativistic Schrodinger equation. An energy level determined by the total angular momentum *j* of the orbiting electron are found to split further due to hyperfine structure effects with the energy difference of 5.9 × 10^{-6} *eV*. This corresponds to a wavelength is 21*cm*. The energy shift between 2 *s* _{1/2} and 2 *p* _{1/2} states due to the effects of vacuum fields on orbiting electron was calculated as 5.52 × 10^{-6} *eV*. We then continue to investigate the change in atomic spectra caused by the finite size nuclear structure effects. The finite-size nuclear structure effect on atomic spectra computed is of order of the scaling factors, *ξ*, *ξ*^{2} and *ξ*^{3} for *n* = 1, *n* = 2 and *n* = 3 atomic energy levels respectively. This showed that as the energy levels increased the effects of the finite – size nucleus on the orbiting electron is diminishing. Therefore the concept of finite nuclear size model has an extremely small impact on atomic spectra. These theoretical findings revealed some of the behavior of atomic spectra which may develop the understanding of spectroscopy and spectroscopic methods.

Keywords

Spectroscopy, Electron Transitions, Schrödinger Equation, Quantum Numbers, Energy Shift, Finite – Size Nucleus

To cite this article

Aliyu Adamu,
Muhammad Hassan,
Mohammed Kyari Dikwa,
Salamatu Ahmad Amshi,
Determination of Nuclear Structure Effects on Atomic Spectra by Applying Rayleigh–Schrödinger Perturbation Theory, *American Journal of Quantum Chemistry and Molecular Spectroscopy*.
Vol. 2, No. 2,
2018, pp. 39-51.
doi: 10.11648/j.ajqcms.20180202.13

Copyright

Copyright © 2018 Authors retain the copyright of this article.

This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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