A New Look at a Nonrelativistic Shell Model: Study of the Mirror Nuclei 17O and 17F in the Symmetries of NCQM

Authors

  • Abdelmadjid Maireche sciences faculty, university of M’sila, Algeria

Keywords:

Schrödinger Equation, Mirror Nuclei And , The Quadratic Hellmann Potential, Noncommutative Space Phase And Bopp’s Shift Method

Abstract

In present work, the 3-dimensional modified Schrödinger equation is analytically solved for nuclei 17O and 17F, which can be modeled as a doubly magic isotope  and , with one additional nucleon (valence) in the  level under modified quadratic Hellmann potential in the symmetries of noncommutative quantum mechanics (NCQM), using the generalized Bopp’s shift method. The new energy eigenvalues and the corresponding modified Hamiltonian operator are calculated in the 3-dimensional noncommutative real space phase (NC: 3D-RSP) symmetries. It is found that the perturbative solutions of the discrete spectrum can be expressed by the Gamma function, the discreet subatomic quantum numbers  and the potential parameters ( ), in addition to the noncommutativity parameters ( and ). The total complete degeneracy of new energy levels of the modified quadratic Hellmann potential changed to become equals to the value  instead of the initial values  in ordinary QM. Our results are in good agreement with the already existing literature in NCQM. 

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Author Biography

Abdelmadjid Maireche, sciences faculty, university of M’sila, Algeria

Laboratory of physical and chemical materials, physics department,

References

G. Audi, O. Bersillon, J. Blachot and A. H. Wapstra, The Nubase evaluation of nuclear and decay properties. Nuclear Physics A 729(1) (2003) 3–128. doi:10.1016/j.nuclphysa.2003.11.001

M. Mousavi and M. R. Shojaei. Calculation of energy and charge radius for doubly-magic nuclei of 41 Ca and 41 Sc with extra nucleon, Chinese Journal of Physics 54(5) (2016) 750–755.doi:10.1016/j.cjph.2016.07.006

M. Mousavi and M. R. Shojaei, Mirror Nuclei of 17O and 17F in Relativistic and Nonrelativistic Shell Model. Adv. High Energy Phys, 2017, 1–5. doi:10.1155/2017/5841701

B. L. Cohen, Concepts of Nuclear Physics, McGraw-Hill, New York, NY, USA, 1971.

Pei-Ming Ho and Hsien-Chung Kao, Noncommutative Quantum Mechanics from Noncommutative Quantum Field Theory, Phys. Rev. Lett. 88 (2002) 151602. DOI: https://doi.org/10.1103/PhysRevLett.88.151602

M. Darroodi, H. Mehraban and H. Hassanabadi, The Klein–Gordon equation with the Kratzer potential in the noncommutative space, Modern Physics Letters A 33(5) (2018) 1850203 (6 pages). doi:10.1142/s0217732318502036

K. P. Gnatenko, Parameters of noncommutativity in Lie-algebraic noncommutative space, Physical Review D. 99(2) (2019) 026009-1. doi:10.1103/physrevd.99.026009

K. P. Gnatenko and V. M.Tkachuk, Weak equivalence principle in noncommutative phase space and the parameters of noncommutativity. Physics Letters A 381(31) (2017) 2463–2469. doi:10.1016/j.physleta.2017.05.056

Abdelmadjid Maireche, The Klein–Gordon equation with modified Coulomb plus inverse-square potential in the noncommutative three-dimensional space. Modern Physics Letters A. 35(5) (2020) 2050015. doi : 10.1142/s0217732320500157

Abdelmadjid Maireche, A Recent Study of Excited Energy Levels of Diatomics for Modified more General Exponential Screened Coulomb Potential: Extended Quantum Mechanics. J. Nano- Electron. Phys. 9(3) (2017) 03021. DOI 10.21272/jnep.9(3).03021

A. E. F. Djemaï and H. Smail, On Quantum Mechanics on Noncommutative Quantum Phase Space. Commun. Theor. Phys. (Beijing, China. 41(6) (2004) 837–844. doi:10.1088/0253-6102/41/6/837

YUAN Yi, LI Kang, WANG Jian-Hua and CHEN Chi-Yi, Spin-1/2 relativistic particle in a magnetic f ield in NC phase space, Chinese Physics C. 34(5) (2010) 543–547. doi:10.1088/1674-1137/34/5/005

O. Bertolami and P. Leal, Aspects of phase-space noncommutative quantum mechanics. Physics Letters B 750 (2015) 6–11. doi:10.1016/j.physletb.2015.08.024

C. Bastos, O. Bertolami, N. C. Dias and J. N. Prata, Weyl–Wigner formulation of noncommutative quantum mechanics. Journal of Mathematical Physics 49(7) (2008) 072101. doi:10.1063/1.2944996

J. Zhang, Fractional angular momentum in non-commutative spaces, Physics Letters B 584(1-2) (2004) 204–209. doi:10.1016/j.physletb.2004.01.049

J. Gamboa, M. Loewe and J. C. Rojas, Noncommutative quantum mechanics, Phys. Rev. D 64 (2001) 067901. DOI: https://doi.org/10.1103/PhysRevD.64.067901.

M. Chaichian, Sheikh-Jabbari and A. Tureanu, Hydrogen Atom Spectrum and the Lamb Shift in Noncommutative QED, Physical Review Letters 86(13) (2001) 2716–2719. doi:10.1103/physrevlett.86.2716.

W. Heisenberg. Letter to R. Peierls (1930), in ’Wolfgang Pauli, Scientific Correspondence’, Vol. III, p.15, Ed. K. von Meyenn - 1985. Springer. : Verlag).

H. Snyder, Quantized Space-Time. Physical Review, 71(1), 1947, 38–41. doi:10.1103/physrev.71.38

Abdelmadjid Maireche, New Relativistic Atomic Mass Spectra of Quark (u, d and s) for Extended Modified Cornell Potential in Nano and Plank’s Scales, J. Nano- Electron. Phys. 8(1) (2016) 01020-1 - 01020-7. DOI: 10.21272/jnep.8(1).01020

Abdelmadjid Maireche, New Bound State Energies for Spherical Quantum Dots in Presence of a Confining Potential Model at Nano and Plank’s Scales, NanoWorld J., 1(4) (2016) 122-129. doi: 10.17756/nwj.2016-016

Abdelmadjid Maireche. Nonrelativistic treatment of Hydrogen-like and neutral atoms subjected to the generalized perturbed Yukawa potential with centrifugal barrier in the symmetries of noncommutative Quantum mechanics. International Journal of Geometric Methods in Modern Physics (2020). DOI: 10.1142/S021988782050067X

Abdelmadjid Maireche, A New Nonrelativistic Investigation for the Lowest Excitations States of Interactions in One-Electron Atoms, Muonic, Hadronic and Rydberg Atoms with Modified Inverse Power Potential, International Frontier Science Letters. 9 (2016) 33-46. DOI: https://doi.org/10.18052/www.scipress.com/IFSL.9.33

Abdelmadjid Maireche, New quantum atomic spectrum of Schrödinger equation with pseudo harmonic potential in both noncommutative three dimensional spaces and phases, Lat. Am. J. Phys. Educ. 9(1) (2015) 1301.

Abdelmadjid Maireche, New Bound States for Modified Vibrational-Rotational Structure of Supersingular Plus Coulomb Potential of the Schrödinger Equation in One-Electron Atoms, International Letters of Chemistry, Physics and Astronomy, 73 (2017) 31-45. DOI : https://doi.org/10.18052/www.scipress.com/ILCPA.73.31

Abdelmadjid Maireche Extended of the Schrödinger Equation with New Coulomb Potentials plus Linear and Harmonic Radial Terms in the Symmetries of Noncommutative Quantum Mechanics. J. Nano- Electron. Phys., 10(6) (2018) 06015-1 - 06015-7. DOI: https://doi.org/10.21272/jnep.10(6).06015

Abdelmadjid Maireche, Investigations on the Relativistic Interactions in One-Electron Atoms with Modified Yukawa Potential for Spin 1/2 Particles, International Frontier Science Letters 11 (2017) 29-44. DOI: https://doi.org/10.18052/www.scipress.com/IFSL.11.29

Abdelmadjid Maireche, Any L-States Solutions of The Modified Schrodinger Equation with Generalized Hellmann–Kratzer Potential Model in The Symmetries of NRNCQM. To Physics Journal, 4 (2O19) 16-32. Retrieved from https://purkh.com/index.php/tophy/article/view/521

Abdelmadjid Maireche, A Nonrelativistic Subatomic Model to Describe a Behavior of 2D Anharmonic Sextic Potential for Atomic Nucleus in the Symmetries of Extended Quantum Mechanics Vol. 11 No 1 (2019) 01024(10pp) .DOI: 10.21272/jnep.11(1).01024

Abdelmadjid Maireche, A New Model for Describing Heavy-Light Mesons in The Extended Nonrelativistic Quark Model Under a New Modified Potential Containing Cornell, Gaussian And Inverse Square Terms in The Symmetries Of NCQM. To Physics Journal, 3 (2019) 197-215. Retrieved from https://purkh.com/index.php/tophy/article/view/500

Abdelmadjid Maireche, General principles of nuclear physics (in Arabic) (University Publications Office Press-Algeria, OPU, 2011 ISBN 978.9961.0.1484.4, https://www.opu-dz.com/portal/

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products, 7th. ed.; Elsevier, edited by Alan Jeffrey (University of Newcastle upon Tyne, England) and Daniel Zwillinger (Rensselaer Polytechnic Institute USA) 2007.

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Published

2020-04-30

How to Cite

Abdelmadjid Maireche. (2020). A New Look at a Nonrelativistic Shell Model: Study of the Mirror Nuclei 17O and 17F in the Symmetries of NCQM. To Physics Journal, 5, 51-67. Retrieved from https://purkh.com/index.php/tophy/article/view/684

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Research Articles