Analytical Investigation of the Single-Particle Energy Spectrum in Magic Nuclei of ⁵⁶Ni and ¹¹⁶Sn



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Submitted Nov 5, 2020
Published Dec 8, 2020
10.24018/ejphysics.2020.2.6.28

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The analytical solutions of the radial D-dimensional Schrödinger equation for the Yukawa potential plus spin-orbit and Coulomb interaction terms are presented within the framework of the Nikiforov-Uvarov method by using the Greene-Aldrich approximation scheme to the centrifugal barrier. The energy eigenvalues obtained are employed to calculate the single-energy spectrum of ⁵⁶Ni and ¹¹⁶Sn for distinct quantum states. We have also obtained corresponding normalized wave functions for the magic nuclei manifested in terms of Jacobi polynomials. However, the energy spectrum without Spin-orbit and Coulomb interaction terms precisely matches the quantum mechanical system of the Yukawa potential field at any arbitrary state.

Keywords: D-dimensional Schrodinger equation, Nikiforov-Uvarov method, spin-orbit and Coulomb interaction terms, Yukawa potential

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