Corrected Analytical Solution of the Generalized Woods-Saxon Potential for Arbitrary $\ell$ States

Abstract

The bound state solution of the radial Schrödinger equation with the generalized Woods-Saxon potential is carefully examined by using the Pekeris approximation for arbitrary $\ell$ states. The energy eigenvalues and the corresponding eigenfunctions are analytically obtained for different $n$ and $\ell$ quantum numbers. The obtained closed forms are applied to calculate the single particle energy levels of neutron orbiting around ${}^{56}$Fe nucleus in order to check consistency between the analytical and Gamow code results. The analytical results are in good agreement with the results obtained by Gamow code for $\ell =0$.

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Cited by in corpus (15)

• The generalized Klein-Gordon oscillator in a Cosmic Space-Time with a Space-Like Dislocation and the Aharonov-Bohm Effect
• Scattering, bound and quasi-bound states of the generalized symmetric Woods-Saxon potential
• Scattering of Klein-Gordon particles in the background of mixed scalar-vector generalized symmetric Woods-Saxon potential
• Bound states of the $D$-dimensional Schrödinger equation for the generalized Woods-Saxon potential
• An Investigation of the Bound State Solutions of the Klein-Gordon Equation for the Generalized Woods-Saxon Potential in Spin Symmetry and Pseudo-spin Symmetry Limits
• Comparative effect of an addition of a surface term to the Woods-Saxon potential on the thermodynamics of a nucleon
• Remarks on the Woods-Saxon Potential
• A statistical mechanical analysis on the bound state solution of an energy-dependent deformed Hulthén potential energy
• Surface Interaction Effects to a Klein-Gordon Particle Embedded in a Woods-Saxon Potential Well in terms of Thermodynamic Functions
• Distributions of the $S$-matrix poles in Woods-Saxon and cut-off Woods-Saxon potentials
• A Comparative Interpretation of the Thermodynamic Functions of a Relativistic Bound State problem proposed with an Attractive or a Repulsive Surface Effect
• A Study of Shell Model Neutron States in ${}^{207,209}Pb$ Using the Generalized Woods-Saxon plus Spin-Orbit Potential
• On the Role of Differentiation Parameter in a Bound State Solution of the Klein-Gordon Equation
• Thermodynamic Properties of a Nucleon under the Generalized Symmetric Woods-Saxon Potential in Flourine 17 Isotope
• Matching polynomial tails to the cut-off Woods-Saxon potential