Thermodynamic functions of Manning-Rosen plus a class of Yukawa potential using Euler MacLaurin Formula

Authors

  • Morris Ramantswana University of South Africa
  • Akpan Ndem Ikot University of Port Harcourt
  • Gaotsiwe Joel Rampho University of South Africa
  • Collins Okon Edet University of Port Harcourt
  • Uduakobong S Okorie Akwa Ibom State University

DOI:

https://doi.org/10.31349/RevMexFisE.19.020204

Keywords:

Nikiforov-Uvarov method; Manning-Rosen potential; Yukawa potential; Thermodynamic functions; Euler MacLaurin formula

Abstract

By employing the Nikiforov-Uvarov (NU) method, we solved the time-independent Schrödinger equation (SE) with Manning-Rosen plus a class of Yukawa potential (MRCYP) model. The eigensolutions expressions were obtained and thermodynamic function expressions were also obtained using Euler MacLaurin formula in closed forms. Numerical results of the energy were obtained with respect to different screening parameters and quantum numbers. In addition, the effects of temperature on the thermodynamic functions were discussed for various screening parameters and quantum states. Unique critical temperatures of entropy and specific heat capacity were seen to exist for the selected screening parameters and quantum numbers. Our results are also in sync with the results in literatures and they promise to be relevant in various areas of studies, including atomic, particle and nuclear physics.

References

C. A. Onate, M. C. Onyeaju, D. T. Bankole and A. N. Ikot, Eigensolution techniques, expectation values and Fisher information of Wei potential function, J. Mol. Mod. 26 (2020) 311, https://doi.org/10.1007/s00894-020-04573-4.

E. Witten, Dynamical breaking of supersymmetry, Nucl. Phys. B. 188 (1981) 513, https://doi.org/10.1016/0550-3213(81)90006-7.

H. Ciftci, R. L. Hall and N. Saad, Asymptotic iteration method for eigenvalue problems, J. Phys. A: Math Gen. 36 (2003) 11807. https://doi.org/10.1088/0305-4470/36/47/008.

G. Chen, The exact solutions of the Schr´”odinger equation with the Morse potential via Laplace transforms Phys. Lett. A. 326 (2004) 55, https://doi.org/10.1016/j.physleta.2004.04.029.

Z. O. Ma and B. W. Xu, Quantum correction in exact quantization rules, Eur. Phys. Lett. 69 (2005) 685. https://doi.org/10.1209/epl/i2004-10418-8.

M. R. Setare and E. Karimi, Algebraic approach to Kratzer potential, Phys. Scri. 75 (2007) 90, https://doi.org/10.1088/0031-8949/75/1/015.

S. H. Dong, Factorization method in Quantum Mechanics, (Armsterdam: Springer, 2007) pp. 150.

J. Y. Liu, G. D. Zhang and C. S. Jia, Calculation of the interaction potential energy curve and vibrational levels for the a 3 Pu+ state of 7Li27 molecule, Phys. Lett. A. 377 (2013) 1444, https://doi.org/10.1016/j.physleta.2013.04.019.

W. C. Qiang and S. H. Dong, Proper quantization rule, Eur. Phys. 89 (2010) 10003. https://doi.org/10.1209/0295-5075/89/10003.

F. A. Serrano, X. Y. Gu and S. H. Dong, Qiang-Dong proper quantization rule and its applications to exactly solvable quantum systems J. Math. Phys. 51 (2010) 082103, https://doi.org/10.1063/1.3466802.

H. M. Tang, G. C. Liang, L. H. Zhang, F. Zhao and C. S. Jia, Diatomic molecule energies of the modified Rosen-Morse potential energy model, Can. J. Chem. 92 (2014) 341, https://doi.org/10.1139/cjc-2013-0563.

C. S. Jia and Y. Jia, Relativistic rotation-vibrational energies for the Cs2 molecule Eur. Phys. J. D. 71 (2017) 3, http://dx.doi.org/10.1140/epjd/e2016-70415-y.

A N. Ikot et al., Bound and Scattering State Solutions of the Klein-Gordon Equation with Deng-Fan Potential in Higher Dimensions, Few-Body Syst. 62 (2021) 9. https://doi.org/10.1007/s00601-021-01693-2.

A. F. Nikiforov, V. B. Uvarov, Special Functions of Mathematical Physics, ed A Jaffe. (BirkhauserVerlag Basel, Germany 1988), p. 317.

C. Y. Chen, D. S. Sun, F. L. Lu, Approximate analytical solutions of Klein-Gordon equation with Hulthen potentials for nonzero angular momentum, Phys. Lett. A. 370 (2007) 219, https://doi.org/10.1016/j.physleta.2007.05.079.

A. N. Ikot, L. E. Akpabio, E. J. Uwah, Bound State Solution of the Klein-Gordon Equation with Hulthen Potential, Electronic. J. Theor. Phys. 8 (2011) 225.

H. Egrifes, R. Sever, Bound-State Solutions of the KleinGordon Equation for the Generalized P T-Symmetric Hulthen Potential, Int. J. Theor. Phys. 46 (2007) 935, https://doi.org/10.1007/s10773-006-9251-8.

W. C. Qiang, R. S. Zhou, Y. Gao, Any l-state solutions of the Klein-Gordon equation with the generalized Hulthen potential, Phys. Lett. A. 371 (2007) 201, https://doi.org/10.1016/j.physleta.2007.04.109.

C. Berkdemir, A. Berkdemir and J. Han, Bound state solutions of the Schrodinger equation for modified Kratzer’s molecular potential, Chem. Phys. Lett. 417 (2006) 326, https://doi.org/10.1016/j.cplett.2005.10.039.

V. H. Badalov, H. I. Ahmadov and S. V. Badalov, Any lstate analytical solutions of the Klein-Gordon equation for the Woods-Saxon potential, Int. J. Mod. Phys. E. 19 (2010) 1463, https://doi.org/10.1142/S0218301310015862.

O. J. Oluwadare, K. J. Oyewumi, and O. A. Babalola, Exact S-Wave Solution of the Klein-Gordon Equation with the DengFan Molecular Potential using the Nikiforov-Uvarov (NU) Method, Afr. Rev. Phys. 7 (2012) 0016.

G. F. Wei, Z. Z. Zhen and S. H. Dong, The relativistic bound and scattering states of the Manning-Rosen potential with an improved new approximate scheme to the centrifugal term, Cent. Eur. J. Phys 7 (2009) 175, https://doi.org/10.2478/s11534-008-0143-9.

C. S. Jia, T. Chen, and S. He, Bound state solutions of the Klein-Gordon equation with the improved expression of the Manning-Rosen potential energy model Phys. Lett. A. 377 (2013) 682, https://doi.org/10.1016/j.physleta.2013.01.016.

G. F. Wei and S. H. Dong, Pseudospin symmetry in the relativistic Manning-Rosen potential including a Pekeris-type approximation to the pseudo-centrifugal term, Phys. lett. B. 686 (2010) 288, https://doi.org/10.1016/j.physletb.2010.02.070.

A. Arda, R. Sever, and C. Tezcan, Effective-mass KleinGordon-Yukawa problem for bound and scattering states, J. Math. Phys. 52 (2011) 092101, https://doi.org/10.1063/1.3641246.

M. Hamzavi, S. M. Ikhdair and K. E. Thylwe, pinless Particles in the Field of Unequal Scalar Vector Yukawa Potentials, Chin. Phys. B. 22 (2013) 040301, https://doi.org/10.1088/1674-1056/22/4/040301.

Z. Wang, Z. W. Long, C. Y. Long and L. Z. Wang, Analytical solutions of position-dependent mass Klein-Gordon equation for unequal scalar and vector Yukawa potentials, Indian J. Phys. 89 (2015) 1059, https://doi.org/10.1007/s12648-015-0677.

A. I. Ahmadov, M. Naem, M. V. Qocayeva and V. A. Tarverdiyeva, Analytical bound-state solutions of the Schrodinger equation for the Manning-Rosen plus Hulthen potential within SUSY quantum mechanics, Int. J. Mod. Phys. A. 33 (2018) 1850021, https://doi.org/10.1142/S0217751X18500215.

A. I. Ahmadov, Sh. M. Nagiyev, M. V. Qocayeva, K. Uzun and V. A. Tarverdiyeva, Bound state solution of the Klein-FockGordon equation with the Hulthen plus a ring-shaped-like potential within SUSY quantum mechanics, Int. J. Mod. Phys. A. 33 (2018) 1850203, https://doi.org/10.1142/S0217751X18502032.

A. I. Ahmadov, S. M. Aslanova, M. Sh. Orujova, S. V. Badalov, and S. H. Dong, Approximate bound state solutions of the Klein-Gordon equation with the linear combination of Hulthen and Yukawa potentials, Phys. Lett. A. 383 (2019) 3010, https://doi.org/10.1016/j.physleta.2019.06.043.

A. I. Ahmadov, M. Demirci, S. M. Aslanova and M. F. Mustamin, Arbitrary l-state solutions of the Klein-Gordon equation with the Manning-Rosen plus a Class of Yukawa potentials, Phys. Lett. A. 384 (2020) 126372, https://doi.org/10.1016/j.physleta.2020.126372.

A. I. Ahmadov, M. Demirci, and S. M. Aslanova, Bound state solutions of the Klein-Fock-Gordon equation with the sum of Manning-Rosen potential and Yukawa potential within SUSYQM, J. Phys. Conf. Ser. 1416 (2019) 012001. https://doi.org/10.1088/1742-6596/1416/1/012001.

C. A. Onate, A. Abolarinwa, S. O. Salawu and N. K. Oladejo, Bound state solutions of the Schrodinger equation and its application to some diatomic molecules, J. Mol. Mod. 26 (2020) 145, https://doi.org/10.1007/s00894-020-04359-8.

S. H. Dong, M. Lozada-Cassou, J. Yu, F. J. Angeles and A. L. Rivera, Hidden symmetries and thermodynamic properties for a harmonic oscillator plus an inverse square potential, Int. J. Quant. Chem. 107 (2007) 366, https://doi.org/10.1002/qua.21103.

C. O. Edet et al., Thermal properties of Deng-Fan-Eckart potential model using Poisson summation approach, J. Math. Chem. (2020) 989. https://doi.org/10.1007/s10910-020-01107-4.

S. H. Dong and M. CruzIrisson, Energy spectrum for a modified Rosen-Morse potential solved by proper quantization rule and its thermodynamic properties, J. Math. Chem. 50 (2012) 881, https://doi.org/10.1007/s10910-011-9931-3.

C. S. Jia, L. H. Zhang and C. W. Wang, Thermodynamic properties for the lithium dimer, Chem. Phys. Lett. 667 (2017) 211, https://doi.org/10.1016/j.cplett.2016.11.059.

X. Q. Song, C. W. Wang and C. S. Jia, Thermodynamic properties for the sodium dimer Chem. Phys. Lett. 673 (2017) 50, https://doi.org/10.1016/j.cplett.2017.02.010.

C. S. Jia et al., Partition function of improved Tietz oscillators, Chem. Phys. Lett. 676 (2017) 150, https://doi.org/10.1016/j.cplett.2017.03.068.

U. S. Okorie, A. N. Ikot, M. C. Onyeaju and E. O. Chukwuocha, Bound state solutions of Schrodinger equation with modified Mobius square potential (MMSP) and its thermodynamic properties, J. Mol. Mod. 24 (2018) 289, https://doi.org/10.1007/s00894-018-3811-8.

C A. Onate, M. C. Onyeaju, U. S. Okorie and A. N. Ikot, Thermodynamic functions for Boron nitride with qdeformed exponential-type potential, Results in Phys. 16 (2020) 102959, https://doi.org/10.1016/j.rinp.2020.102959; 58 (2020) 989, https://doi.org/10.1007/s10910-020-01107-4.

U. S. Okorie et al., Energies Spectra and Thermodynamic Properties of Hyperbolic Poschl-Teller Potential (HPTP) Model, ¨Int. J. Thermophys. 41 (2020) 91, https://doi.org/10.1007/s10765-020-02671-2.

M. Angelova and A. Frank, Algebraic Approach to Thermodynamic Properties of Diatomic Molecules, Phys. Atomic Nuclei. 68 (2005) 1625, https://doi.org/10.1134/1.2121908.

G. Valencia-Ortega and L. A. Arias-Hernandez, Thermodynamic properties of diatomic molecule systems under SO(2, 1)-anharmonic Eckart potential, Int. J. Quant. Chem. 118 (2018) e25589, https://doi.org/10.1002/qua.25589.

A. Boumali, The statistical properties of q-deformed Morse potential for some diatomic molecules via Euler-MacLaurin

method in one dimension, J. Math. Chem. 56 (2018) 1656, https://doi.org/10.1007/s10910-018-0879-4.

G. Arfken, Mathematical Methods for Physicists, 3rd Edn. (Academic Press, Orlando, 1985), pp. 327-338.

K. Chabi and A. Boumali, Thermal properties of threedimensional Morse potential for some diatomic molecules via Euler-Maclaurin approximation, Rev. Mex. Fis. 66 (2020) 110. https://doi.org/10.31349/revmexfis.66.110.

A. N. Ikot et al., Exact and Poisson summation thermodynamic properties for diatomic molecules with shifted Tietz potential, Ind. J. Phys. 93 (2019) 1171, https://doi.org/10.1007/s12648-019-01375-0.

U. S. Okorie, A. N. Ikot, M. C. Onyeaju and E. O. Chukwuocha, A study of thermodynamic properties of quadratic exponentialtype potential in D-dimensions, Rev. Mex. Fis. 64 (2019) 608. https://doi.org/10.31349/revmexfis.64.608.

U. S. Okorie, A. N. Ikot, E. O. Chukwuocha and G. J. Rampho, Thermodynamic properties of improved deformed exponentialtype potential (IDEP) for some diatomic molecules, Results in Phys. 17 (2020) 103078, https://doi.org/10.1016/j.rinp.2020.103078.

R. Horchani and H. Jelassi, Effect of quantum corrections on thermodynamic properties for dimers, Chem. Phys. 532 (2020) 110692, https://doi.org/10.1016/j.chemphys.2020.110692.

C. O. Edet et al., Persistent Current, Magnetic Susceptibility, and Thermal Properties for a Class of Yukawa Potential in the Presence of External Magnetic and Aharanov-Bohm Fields, Int. J. Thermophys. 42 (2021) 138, https://doi.org/10.1007/s10765-021-02891-0.

R. Horchani, S. A. Safii, H. Friha and H. Jelassi, int. J. Thermophys. 42 (2021) 84. https://doi.org/10.1007/s10765-021-02839-4.

R. Horchani, H. Jelassi, A. N. Ikot and U. S. Okorie, Rotation vibration spectrum of potassium molecules via the improved generalized Poschl-Teller oscillator, ¨ Int. J. Quant. Chem. E. 26558 (2020) e26558, https://doi.org/10.1002/qua.26558.

R. Horchani, N. Al-Kindi and H. Jelassi, Ro-vibrational energies of caesium molecules with the Tietz-Hua oscillator, Mol. Phys. E. 119 (2020) e1812746, https://doi.org/10.1080/00268976.2020.1812746.

A. N. Ikot et al., J. Low temp. Phys. 202 (2021) 269. https://doi.org/10.1007/s10909-020-02544-w.

X. Y. Gu and S. H. Dong, Energy spectrum of the ManningRosen potential including centrifugal term solved by exact and proper quantization rules, J. Math. Chem. 49 (2011) 2053, https://doi.org/10.1007/s10910-011-9877-5.

M. F. Manning and N. Rosen, A potential function for the vibrations of diatomic molecules, Phys. Rev. 44 (1933) 953.

W. C. Qiang and S. H. Dong, Analytical approximations to the solutions of the Manning-Rosen potential with centrifugal term,

Phys. lett. 368 (2007) 13, https://doi.org/10.1016/j.physleta.2007.03.057.

G. F. Wei and S. H. Dong, Approximately analytical solutions of the Manning-Rosen potential with the spin-orbit coupling term and spin symmetry, Phys. lett. A. 373 (2008) 49, https://doi.org/10.1016/j.physleta.2008.10.064.

D. J. Griffiths, Introduction to Quantum Mechanics, (Prentice Hall, Upper Saddle River, New Jersey, 1995), 07458.

G. F. Wei and S. H. Dong, Approximately analytical solutions of the Manning-Rosen potential with the spin-orbit coupling term and spin symmetry, Phys. lett. A. 373 (2008) 49, https://doi.org/10.1016/j.physleta.2008.10.064.

R. L. Greene and C. Aldrich, Variational wave functions for a screened Coulomb potential, Phys. Rev. A. 14 (1976) 2363, https://doi.org/10.1103/PhysRevA.14.2363.

M. Servatkhah, R. Khordad and A. Ghanbari, Accurate Prediction of Thermodynamic Functions of H2 and LiH Using Theoretical Calculations, Int. J. Thermophys. 41 (2020) 37, https://doi.org/10.1007/s10765-020-2615-0.

R. Khordad and A. Ghanbari, Theoretical Prediction of Thermodynamic Functions of TiC: Morse Ring-Shaped Potential, J. Low Temp. Phys. 199 (2020) 1198, https://doi.org/10.1007/s10909-020-02368-8.

A. N. Ikot et al., Thermodynamics properties of diatomic molecules with general molecular potential, Pramana J. Phys. 90 (2018) 22, https://doi.org/10.1007/s12043-017-1510-0.

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Published

2022-04-30

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[1]
M. Ramantswana, A. N. Ikot, G. J. Rampho, C. O. Edet, and U. S. Okorie, “Thermodynamic functions of Manning-Rosen plus a class of Yukawa potential using Euler MacLaurin Formula ”, Rev. Mex. Fis. E, vol. 19, no. 2 Jul-Dec, pp. 020204 1–, Apr. 2022.

Issue

Vol. 19 No. 2 Jul-Dec (2022): Revista Mexicana de Física E

Section

02 Education in Physics

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Copyright (c) 2022 Morris Ramantswana, Akpan Ndem Ikot, Gaotsiwe Joel Rampho, Collins Okon Edet, Uduakobong S Okorie

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