Determination of Energy Spectra By Using Proper Quantization Rule of Woods-Saxon Potential

Year 2021, , 1287 - 1293, 01.09.2021

Rezvan Rezaeizadeh , Niloufar Zoghi-foumani , Abbas Ghasemizad , Aybaba Hançerlioğulları

https://doi.org/10.2339/politeknik.770330

Abstract

In this study, the energy spectra of Schrodinger equation for non-zero l values considering Woods Saxon potential (WSP) is calculated using proper quantization rule, then the binding energies (BE) of random light nuclei is obtained and the optimized potential parameters such as potential depth (V0) and surface thickness (a) are found. In order to calculate the energy levels of the nuclei with WSP, the PQR method was used, which has not been considered before. In quantum mechanics, the exact solution of energy systems, momentum, and quantum states can be found using the proper quantization rule(PQR) method.Using the Matlab calculation program, we have achieved numerical values of the energy spectrum for random light nuclei and compared the result with the experimental Nuclear Data Center (NDC) values. In addition, we found potential depth and surface thickness for four light nuclei. Correlations between the light nuclei show the facts about the nuclear structure characteristics, origin, and energies of these nuclei. Pearson’s correlation coefficient is accepted as the most common correlation coefficient. According to the values of Pearson correlation coefficients, it is observed that there is a significant positive correlation between the nucleons examined. Finally, we plot the E-V0-a diagrams for those values to optimize and provide the appropriate coefficients. It is shown that there is a good agreement between the results of this work and experimental values.

Keywords

Schrodinger equation, woods saxon potential, proper quantization rule, binding energy

References

• [1] Qiang W.C., Dong S. H. “Proper quantization rule” Europhysics Letters Association, 89, 10003, (2010).
• [2] Serrano F. A., Xiao-Yan Gu, Dong S.H,”Qiang–Dong proper quantization rule and its applications to exactly solvable quantum systems”,Journal of Mathematical Physics 51, 082103,(2010).
• [3] Ikhdair S. M., An improved approximation scheme for the centrifugal term and the Hulthén potential”,The European Physical Journal A , 39:307, (2009).
• [4] Cooper F., Khare A., Sukhatme U.,” Supersymmetry and quantum mechanics”Physics Reports, 251, 267, (1995).
• [5] Comtet A., Bandrauk A., Campbell D., “ Exactness of semiclassical bound state energies for supersymmetric quantum mechanics”,Physics Letters B,150: 159, (1985). [6] Nikiforov,A.F.and Uvarov,V.B.," Special Functions of MathematicalPhysics Birkhauser,Basel., (1988).
• [7] Zoghi F. N., Shojaei M. R. , Rajabi A. A.,”A new non-microscopic study of cluster structures in light alpha-conjugate nuclei”,Chinese Physics C,41: 014104, (2017).
• [8] Infeld L. , Hull T. E., “The Factorization Method”, Reviews of Modern Physics - Physical Review Journals,23, 21 (1951).
• [9] Ma Z. Q., Xu B. W., “Quantum correction in exact quantization rules”, European Physical Journal letter,691- 685, (2005).
• [10] Ma Z. Q., Xu B. W., “Exact quantization rule and the invariant”, Acta Physica Sinica. ,55: 1571, (2006).
• [11] Gu X.Y., Dong S.H, “From Bohr-Sommerfeld semiclassical quantization rule to Qiang Dong proper quantization rule” in Horizons in World Physics 272, Nova Science Publishers, (2011).
• [12] Ou Y. C., Cao Z. Q., Shen Q. S., “Formally exact quantization condition for nonrelativistic quantum systems”, The Journal of Chemical Physics.,121: 8175, (2004). [13] Schiff L. I., “Quantum Mechanics”, 3rd ed. McGraw-Hill, New York, (1968).
• [14] Mandelzweig V. B,” Quasilinearization method: Nonperturbative approach to physical problems”Physics of Atomic Nuclei 68: 1227–1258, (2005).
• [15] Mandelzweig V. B., Tabakin F., “Quasilinearization approach to nonlinear problems in physics with application to nonlinear ODEs” Computer Physics Communications ,141(2): 268-281, (2001).
• [16] Hassanabadi H., Hamzavi1M.,Zarrinkamar S,A. Rajabi ,” Exact solutions of N-Dimensional Schrödinger equationfor a potential containing coulomb and quadratic terms”, International Journal of the Physical Sciences ,6(3): 583-586, (2011).
• [17] Krivec R. , Mandelzweig V. B., “Quasilinearization approach to quantum mechanics” Computer Physics Communications. ,152: 165, (2003).
• [18] Mandelzweig V. B., “Comparison of quasilinear and WKB approximations”, Annals of Physics. 321: 2810, (2006).
• [19] Liverts E. Z., Drukarev E. G., Mandelzweig V. B., “Accurate analytic presentation of solution of the Schrödinger equation with arbitrary physical potential”, Annals of Physics., 322, 2958, (2007).
• [20] Liverts E. Z.,, Mandelzweig V. B, Tabakin F., “Analytic calculation of energies and wave functions of the quartic and pure quartic oscillators”,Journal of Mathematical Physics,47: 062109, (2006).
• [21] Liverts E. Z , Mandelzweig V. B , “Accurate analytic presentation of solution of the Schrödinger equation with arbitrary physical potential: Excited states”,Annals of Physics.,323, 2913, (2008).
• [22] Liverts E. Z , Mandelzweig V. B, “Approximate analytic solutions of the Schrödinger equation for the generalized anharmonic oscillator”,Physica Scripta,77, 025003, (2008).
• [23]Liverts E. Z , Mandelzweig V. B, “Analytical computation of amplification of coupling in relativistic equations with Yukawa potential” Annals of Physics ,324, 388, (2009).
• [24] Mandelzweig V. B, “Quasilinearization method and its verification on exactly solvable models in quantum mechanics”, Journal of Mathematical Physics,,40: 62-66, (1999).
• [25] Cao Yin Z.Q., Shen Q.S., “Why SWKB approximation is exact for all SIPs ”,Annals of Physics , 325:528, (2010).
• [26] Qiang W.C., Dong S.H., “Arbitrary l-state solutions of the rotating Morse potential through the exact quantization rule method”, Physics Letters A, 363: 169, (2007).
• [27] Qiang W.C. , Zhou R.S., Gao Y., “Application of the exact quantization rule to the relativistic solution of the rotational Morse potential with pseudospin symmetry”,Journalof PhysicsA:Mathematical and Theoretical,40:1677, (2007).
• [28] Dong S.H, Gonzalez C. A., “Energy spectra of the hyperbolic and second Pöschl–Teller like potentials solved by new exact quantization rule”, Annals of Physic,323: 1136, (2008).
• [29] Gu X.Y., Dong S.H. , Ma Z.Q., “Energy spectra for modified Rosen–Morse potential solved by the exact quantization rule”Journal of Physics A: Mathematical and Theoretica42, 035303, (2009) .
• [30] Ma Z.Q., Gonzalez C. A , Xu B.W., Dong S.H. ,”Energy spectrum of the trigonometric Rosen–Morse potential using an improved quantization rule”,Physics Letters A, 371, 180, (2007).
• [31] Gu X.Y., Dong S.H., The improved quantization rule and the Langer modification”, Physics Letters A, 372, 1972, (2008).
• [32] Qiang W.C, Dong S.H,” Proper quantization rule”,Europhysics Letters,EPL 89: 10003, (2010).
• [33] Gu X.Y., Dong S.H., Chapter 8 in Horizons in World Physics , 272, Nova Science Publishers, (2011).
• [34] Serrano F.A., Cruz I. M., “Energy spectrum for a modified Rosen-Morse potential solved by proper quantization rule and its thermodynamic properties”., Journal of Mathematical Chemistry , 50:881–892, (2012).
• [35] Yang N., Proceedings of the Monopole Meeting, Trieste, Italy; Eds;World Scientific:Singapor, 237, (1982).
• [36]Abdi H.,Williams L.J, Principal component analysis,Wiley Interdisciplinary Reviews: Computational Statistics, 2: 433, (2010).