Computational Studies of Energy and Expectation Values of Modified Yukawa Potential (MYP) for some Diatomic Molecules

Authors

  • Uduakobong S. Okorie Department of Physics, Akwa Ibom State University, Ikot Akpaden, Mkpat Enin, Nigeria
  • Nsikak E. Ekpenyong Department of Physics, Akwa Ibom State University, Ikot Akpaden, Mkpat Enin, Nigeria
  • Sylvester A. Ekong Department of Physics, Akwa Ibom State University, Ikot Akpaden, Mkpat Enin, Nigeria
  • Inyang A. Akpabio Department of Physics, Akwa Ibom State University, Ikot Akpaden, Mkpat Enin, Nigeria
  • Ubong A. Iboh Department of Physics, Akwa Ibom State University, Ikot Akpaden, Mkpat Enin, Nigeria
  • Etebong E. Ibekwe Department of Physics, Akwa Ibom State University, Ikot Akpaden, Mkpat Enin, Nigeria
  • Ubong W. Robert Department of Physics, Akwa Ibom State University, Ikot Akpaden, Mkpat Enin, Nigeria
  • Akpan N. Ikot Theoretical Physics Group, Department of Physics, University of Port Harcourt, Choba, Nigeria

Keywords:

Schrödinger equation (SE), Modified Yukawa Potential (MYP), Expectation Values, Diatomic molecules (DMs), Energy values

Abstract

The modified Yukawa potential energy function is known to be a very lofty model due to its potency in predicting the behaviour of different atoms and molecules. The aim of this study is to establish numerical energies and expectation values of some diatomic molecules confined in modified Yukawa potential. By employing the basic ideas of non-relativistic quantum mechanics, the radial Schrödinger equation (SE) with modified Yukawa potential (MYP) is solved using the asymptotic iteration method (AIM). We explicitly obtained the energy value expression and their correspond-ding normalized eigen - functions in closed form for some diatomic molecules (DMs) such as hydrogen dimer (H2), lithium hydride (LiH) and hydrogen chloride (HCl), with the help of the Greene - Aldrich-type approximation scheme. Using the Hellman-Feynman theorem (HFT), we obtained the expressions for the expectation values of the selected DMs. The numerical results of the energies and expectation values of the DMs with varying quantum numbers are further presented. In addition, the graphical plots of the energies and expectation values as functions of quantum numbers have been discussed extensively. It is observed that the energies and expectation values of MYP depend greatly on the quantum numbers for the selected DMs. Our results show a great correlation when compared to other works in available literature.

         Views | Downloads: 154 / 150

References

Arda, A. (2017). Analytical solution of two-body spinless Salpeter equation for Hellmann potential, Indian Journal of Physics, vol. 91, no. 8, pp. 903–907.

Bayrak, O. and Boztosun, I. (2007). Bound state solutions of the Hulthénpotential by using the asymptotic iteration method, Physica Scripta, vol. 76, pp. 92– 96.

Chabi, K. and Boumali, A. (2020). Thermal properties of three dimensional Morse potential for some diatomic molecules via Euler-Maclaurin approximation, Revista Mexicana De Física, vol. 66, no. 1, pp. 110–120.

Chen, H., Zare, S., Hassanabadi, H. and Long,Z. W. (2022).Quantum description of the moving magnetic quadrupole moment interacting with electric field configurations under the rotating background with the screw dislocation, Indian Journal of Physics, vol. 96, pp. 4219 – 4229.

Ciftci, H., Hall, R.L. and Saad, N. (2005). Asymptotic iteration method for eigenvalue problems, Physics Letter A, vol. 340, pp. 288.

Donfack, B. and Fotue, A. J. (2021). Effects of spin orbit interaction (SOI) on the thermodynamic properties of a quantum pseudodot, Journal of Low Temperature Physics, vol. 204, pp. 206 – 222.

Dong, S. H. (2007). Factorization Method in Quantum Mechanics, Spinger, Netherlands.

Dong, S. H., Morales, D. and Garcia-Ravelo, J.(2007). Exact Quantization Rule and its Applications to Physical Potentials, International Journal of Modern Physics E, vol. 16, no. 1, pp. 189 –198.

Dong, S. H. and Cruz-Irisson, M. (2012). Energy spectrum for a modified Rosen-Morse potential solved by proper quantization ruleand its thermodynamic properties, Journal of Mathematical Chemistry, vol. 50, pp. 881 – 892.

Duc, N. B., Hung, N. V.,Khoa, H. D., Vuong, H. Q. and Tien, T. S. (2018). Thermodynamic properties and an-harmonic effects in XAFS based on anharmonic correlated Debye model Debye–Waller factors, Advances in Materials Science and Engineering, vol. 2018, Article ID 3263170, 9 pages.

Edet, C. O., Okorie,U. S., Osobonye, G. T., Ikot, A. N., Rampho, G. J. and Server,R. (2020). Thermal properties of Deng–Fan–Eckart potential model using Poisson summation approach, Journal of Mathematical Chemistry, 58, 989.

Eyube, E. S., Timtere, P. and Yerima, J. B. (2022). Potential parameters, ro-vibrational energy spectra, and expectation values of the improved deformed exponential-type potential, Canadian Journal of Physics, vol. 100, pp. 351 – 361.

Falaye, B. J., Oyewumi, K. J., Ikhdair, S. M. and Hamzavi, M. (2014). Eigensolution techniques, their applications and Fisherʼs information entropy of the Tietz–Wei diatomic molecular model, Physica Scripta, vol. 89, 115204 (27 pages).

Feymann, R. P. (1939). Forces in Molecules, Physical Review, vol. 56, 340 (4 pages).

Gradshteyn, I. S. and Ryzhik, I. M. (2007). Table of Integrals, Series and Products, 7th Edn. Elsevier, London, UK.

Greene, R. L. and Aldrich, C. (1976). Variational wave functions for a screened Coulomb potential, Physical Review A, vol. 14, no. 6, pp. 2363 – 2366.

Huber, K. P. and Herzberg, G. (1979). Constants of diatomic molecules, in Molecular Spectra and Molecular Structure, Springer, pp. 8 – 689.

Ikhdair, S. M. and Hamzavi, M. (2012). Relativistic New Yukawa-like Potential and Tensor Coupling, Few-Body Systems, vol. 53, 487.

Ikhdair, S. M. and Falaye, B. J. (2014). A charged spinless particle in scalar–vector harmonic oscillators with uniform magnetic and Aharonov–Bohm flux fields, Journal of the Association of Arab Universities for Basic and Applied Sciences, vol. 16, pp. 1–10.

Ikot, A. N., Maghsodi, E., Zarrinkamar, S., Salehi, N. and Hassanabadi, H. (2013). Pseudospin and Spin Symmetry of Dirac-Generalized Yukawa Problems with a Coulomb-like Tensor Interaction via SUSYQM, International Journal of Modern physics E, vol. 22, no. 7, 1350052 (25 pages).

Ikot, A. N., Chukwuocha,E. O., Onyeaju,M. C., Onate,C. N., Ita, B. I. and Udoh,M. E. (2018). Thermodynamics properties of diatomic molecules with general molecular potential, Pramana Journal of Physics, 90, 22.

Ikot, A. N., Okorie, U. S., Sever, R. and Rampho, G. J. (2019). Eigen solution, expectation values and thermodynamic properties of the screened Kratzer potential, The European Physical Journal Plus, vol. 134, no. 8, 386, (18 pages).

Ikot, A. N., Okorie,U. S., Amadi, P. O., Edet, C. O., Rampho, G. J. and Sever, R. (2021). The Nikiforov–Uvarov-Functional Analysis (NUFA) Method: A New Approach for Solving Exponential-Type Potentials, Few-Body Systems, 62, 9.

Khordad, R., Fathizadeh, N., Davatolhagh, S. and Jafari, A. R. (2012). Hydrogenic impurity states in a spherical quantum antidot: spin-orbit interaction, relativistic correction, and diamagnetic susceptibility, The European Physical Journal B, vol. 85, no. 10, 1– 6.

Khordad, R., Edet, C. O. and Ikot, A. N. (2022). Application of Morse Potential and Improved Deformed Exponential-type Potential (IDEP) model to predict Thermodynamic Properties of Diatomic Molecules, International Journal of Modern Physics C, vol. 33, no. 8, 2250106.

Liu, G., Guo, K., Hassanabadi, H. and Lu, L. (2012). Linear and nonlinear optical properties in a disk-shaped quantum dot with a parabolic potential plus a hyperbolic potential in a static magnetic field, Physica B: Condensed Matter, vol. 407, no. 17, pp. 3676–3682.

Nikiforov, A. F. and Uvarov, V. B. (1988).Special Functions of Mathematical Physics. Birkhauser, Basel.

Okon, I. B., Popoola, O. and Isonguyo, C. N. (2017). Approximate Solutions of Schrodinger Equation with Some Diatomic Molecular Interactions Using Nikiforov-Uvarov Method, Advances in High Energy Physics, vol. 2017, Article ID 9671816, 24 pages.

Okon, I. B., Onate, C. A., Omugbe, E., Okorie, U. S., Antia, A. D., Onyeaju, M. C., Li, C. W. and Araujo, J. (2022). Approximate Solutions, Thermal Properties, and Superstatistics Solutions to Schrödinger Equation, Advances in High Energy Physics, 5178247, 18 pages.

Okorie, U. S. (2017). Effects of Confinement Energies on Lead Sulphide and Indium Phosphide Quantum Dots within Brus Equation Model, AASCIT Journal of Physics, vol. 3, no. 4, pp. 28 – 35.

Okorie, U. S. and Iboh, U. A. (2018).The Influence of Quantum Dot Size on Confinement Energy: A Modified Single Band Toy Model Approach, International Journal of Modern Physics and Application, vol. 5, no. 1, pp. 1-5.

Okorie, U. S., Ibekwe, E. E., Ikot, A. N., Onyeaju, M. C. and Chukwuocha, E. O. (2018). Thermodynamic properties of the modified Yukawa potential, Journal Of The Korean Physical Society, vol. 73, no. 9, pp. 1211–1218.

Oluwadare, O. J. and Oyewumi, K. J. (2018a).Approximate scattering state solutions of DKPE and SSE with Hellmann potential, Advances in High Energy Physics, vol. 2018, Article ID 5214041, 8 pages.

Oluwadare, O. J. and Oyewumi, K. J. (2018b). Energy spectra and the expectation values of diatomic moleculesconfined by the shifted Deng-Fan potential, European Physical Journal Plus, vol.133, 422 (14 pages).

Oluwadare, O. J., Ilesanmi, E. O., Abiola, T. O., Olubosede, O., Odo, E. A. and Ajibade, S. O. (2022a). Investigating Some Diatomic Molecules Bounded by the Two-Dimensional Isotropic Oscillator plus Inverse Quadratic Potential in an External Magnetic Field, Advances in High High Energy Physics. Article ID 6565048, 14 pages.

Oluwadare, O. J., Oyewumi, K. J. and Abiola, T. O. (2022b). Thermodynamic properties of some diatomic molecules bounded by an harmonic oscillating system, Indian Journal of Physics, vol. 96, no. 7, pp. 1921–1928.

Onate, C. A., Okon, I. B., Eyube, E. S., Bankole, D. T., Omugbe, E., Olayinka, A. S., Onyeaju, M. C., Ebomwonyi, O. and Odeyemi, O. E. (2022). Analytical study of Gallium Halides for Poschl-Teller Potential Model, Chemical Physics Impact, vol. 5, 100123.

Osobonye, G. T., Adekanmbi, M., Ikot, A. N., Okorie, U. S. and Rampho, G. J. (2021). Thermal Properties of Anharmonic Eckart Potential model using Euler–MacLaurin Formula, Pramana Journal of Physics, 95, 98.

Oyewumi, K. J. (2005). Analytical Solutions of the Kratzer-Fues Potential in an Arbitrary number of Dimensions, Foundations of Physics Letters, vol. 18, no. 1, pp. 75 – 84.

Oyewumi,K. J., Falaye, B. J., Onate, C. A., Oluwadare,O. J. and Yahya,W. A. (2014). Thermodynamic Properties and the Appropriate Solutions of the Schrodimger Equation with the Shifted Deng-Fan Potential Model, Molecular Physics, vol. 112, 127.

Oyewumi, K. J. and Oluwadare, O. J. (2017). Relativistic energies and scattering phase shifts for the fermionic particles scattered by hyperbolical potential with the pseudo (spin) symmetry, Advances in High Energy Physics, vol. 2017, Article ID 1634717, 11 pages.

Qin, Z., Bai, T. R. and Liu, L. H.(2021). Line Lists for the transitions of CP. Journal of Quantitative Spectroscopy and Radiative Transfer. 258, 107352.

Rajabi, A. A. and Hamzavi, M. (2013). Relativistic effect of external magnetic and Aharonov Bohm fields on the unequal scalar and vector Cornell model, The European Physical Journal Plus, vol. 128, no. 1, pp. 1–6.

Rezvani, F. and Shojaei,M. R. (2017).Energy levels of weakly bound nuclei with relativistic effects, Scientific Bulletin-University Politehnica of Bucharest Series A, vol. 79, no. 3, pp. 193–202.

Rezvani, F. and Shojaei,M. R. (2018). Relativistic effects in the study of weakly bound 17F and 11Be nuclei, Pramana Journal of Physics, vol. 90, no. 2, pp. 1–8.

Saravanan, S., Peter, A. J. and Lee, C. (2015). Combined effects of magnetic and electric fields on the interband optical transitions in InAs/InP quantum wire, Physica E: Low dimensional Systems and Nanostructures, vol. 67, pp. 99–104.

Zhang, L. H., Li, X. P. and Jia, C. S. (2011).Approximate Solutions of the Schrodinger Equation with the Generalized Morse Potential Model including the Centrifugal Term, International Journal of Quantum Chemistry, vol. 111,1870.

Downloads

Published

2022-12-28

How to Cite

Okorie, U. S., Ekpenyong, N. E., Ekong, S. A., Akpabio, I. A., Iboh, U. A., Ibekwe, E. E., … Ikot, A. N. (2022). Computational Studies of Energy and Expectation Values of Modified Yukawa Potential (MYP) for some Diatomic Molecules. Researchers Journal of Science and Technology, 2(3), 68–83. Retrieved from https://rejost.com.ng/index.php/home/article/view/42

Issue

Vol. 2 No. 3 (2022): Reseachers Journal of Science and Technology

Section

Articles

License

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.