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

Aliyu Adamu; Muhammad Hassan; Mohammed Kyari Dikwa; Salamatu Ahmad Amshi

doi:doi:10.11648/j.ajqcms.20180202.13

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

Aliyu Adamu, Muhammad Hassan, Mohammed Kyari Dikwa, Salamatu Ahmad Amshi

Published in American Journal of Quantum Chemistry and Molecular Spectroscopy (Volume 2, Issue 2)

Received: 29 August 2018 Accepted: 11 September 2018 Published: 11 January 2019

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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 21cm. 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, ξ² and ξ³ 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.

Published in	American Journal of Quantum Chemistry and Molecular Spectroscopy (Volume 2, Issue 2)
DOI	10.11648/j.ajqcms.20180202.13
Page(s)	39-51
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

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

References

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Aliyu Adamu, Muhammad Hassan, Mohammed Kyari Dikwa, Salamatu Ahmad Amshi. (2019). Determination of Nuclear Structure Effects on Atomic Spectra by Applying Rayleigh–Schrödinger Perturbation Theory. American Journal of Quantum Chemistry and Molecular Spectroscopy, 2(2), 39-51. https://doi.org/10.11648/j.ajqcms.20180202.13

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ACS Style

Aliyu Adamu; Muhammad Hassan; Mohammed Kyari Dikwa; Salamatu Ahmad Amshi. Determination of Nuclear Structure Effects on Atomic Spectra by Applying Rayleigh–Schrödinger Perturbation Theory. Am. J. Quantum Chem. Mol. Spectrosc. 2019, 2(2), 39-51. doi: 10.11648/j.ajqcms.20180202.13

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AMA Style

Aliyu Adamu, Muhammad Hassan, Mohammed Kyari Dikwa, Salamatu Ahmad Amshi. Determination of Nuclear Structure Effects on Atomic Spectra by Applying Rayleigh–Schrödinger Perturbation Theory. Am J Quantum Chem Mol Spectrosc. 2019;2(2):39-51. doi: 10.11648/j.ajqcms.20180202.13

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@article{10.11648/j.ajqcms.20180202.13,
  author = {Aliyu Adamu and Muhammad Hassan and Mohammed Kyari Dikwa and Salamatu Ahmad Amshi},
  title = {Determination of Nuclear Structure Effects on Atomic Spectra by Applying Rayleigh–Schrödinger Perturbation Theory},
  journal = {American Journal of Quantum Chemistry and Molecular Spectroscopy},
  volume = {2},
  number = {2},
  pages = {39-51},
  doi = {10.11648/j.ajqcms.20180202.13},
  url = {https://doi.org/10.11648/j.ajqcms.20180202.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajqcms.20180202.13},
  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 21cm. 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, ξ2 and ξ3 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.},
 year = {2019}
}

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TY  - JOUR
T1  - Determination of Nuclear Structure Effects on Atomic Spectra by Applying Rayleigh–Schrödinger Perturbation Theory
AU  - Aliyu Adamu
AU  - Muhammad Hassan
AU  - Mohammed Kyari Dikwa
AU  - Salamatu Ahmad Amshi
Y1  - 2019/01/11
PY  - 2019
N1  - https://doi.org/10.11648/j.ajqcms.20180202.13
DO  - 10.11648/j.ajqcms.20180202.13
T2  - American Journal of Quantum Chemistry and Molecular Spectroscopy
JF  - American Journal of Quantum Chemistry and Molecular Spectroscopy
JO  - American Journal of Quantum Chemistry and Molecular Spectroscopy
SP  - 39
EP  - 51
PB  - Science Publishing Group
SN  - 2994-7308
UR  - https://doi.org/10.11648/j.ajqcms.20180202.13
AB  - 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 21cm. 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, ξ2 and ξ3 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.
VL  - 2
IS  - 2
ER  -

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Author Information

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

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Aliyu Adamu, Muhammad Hassan, Mohammed Kyari Dikwa, Salamatu Ahmad Amshi. (2019). Determination of Nuclear Structure Effects on Atomic Spectra by Applying Rayleigh–Schrödinger Perturbation Theory. American Journal of Quantum Chemistry and Molecular Spectroscopy, 2(2), 39-51. https://doi.org/10.11648/j.ajqcms.20180202.13

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ACS Style

Aliyu Adamu; Muhammad Hassan; Mohammed Kyari Dikwa; Salamatu Ahmad Amshi. Determination of Nuclear Structure Effects on Atomic Spectra by Applying Rayleigh–Schrödinger Perturbation Theory. Am. J. Quantum Chem. Mol. Spectrosc. 2019, 2(2), 39-51. doi: 10.11648/j.ajqcms.20180202.13

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AMA Style

Aliyu Adamu, Muhammad Hassan, Mohammed Kyari Dikwa, Salamatu Ahmad Amshi. Determination of Nuclear Structure Effects on Atomic Spectra by Applying Rayleigh–Schrödinger Perturbation Theory. Am J Quantum Chem Mol Spectrosc. 2019;2(2):39-51. doi: 10.11648/j.ajqcms.20180202.13

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@article{10.11648/j.ajqcms.20180202.13,
  author = {Aliyu Adamu and Muhammad Hassan and Mohammed Kyari Dikwa and Salamatu Ahmad Amshi},
  title = {Determination of Nuclear Structure Effects on Atomic Spectra by Applying Rayleigh–Schrödinger Perturbation Theory},
  journal = {American Journal of Quantum Chemistry and Molecular Spectroscopy},
  volume = {2},
  number = {2},
  pages = {39-51},
  doi = {10.11648/j.ajqcms.20180202.13},
  url = {https://doi.org/10.11648/j.ajqcms.20180202.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajqcms.20180202.13},
  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 21cm. 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, ξ2 and ξ3 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.},
 year = {2019}
}

Copy | Download

TY  - JOUR
T1  - Determination of Nuclear Structure Effects on Atomic Spectra by Applying Rayleigh–Schrödinger Perturbation Theory
AU  - Aliyu Adamu
AU  - Muhammad Hassan
AU  - Mohammed Kyari Dikwa
AU  - Salamatu Ahmad Amshi
Y1  - 2019/01/11
PY  - 2019
N1  - https://doi.org/10.11648/j.ajqcms.20180202.13
DO  - 10.11648/j.ajqcms.20180202.13
T2  - American Journal of Quantum Chemistry and Molecular Spectroscopy
JF  - American Journal of Quantum Chemistry and Molecular Spectroscopy
JO  - American Journal of Quantum Chemistry and Molecular Spectroscopy
SP  - 39
EP  - 51
PB  - Science Publishing Group
SN  - 2994-7308
UR  - https://doi.org/10.11648/j.ajqcms.20180202.13
AB  - 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 21cm. 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, ξ2 and ξ3 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.
VL  - 2
IS  - 2
ER  -

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