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 $\ell =0$.

References in corpus (4)

• Any $l$-state solutions of the Hulthén potential by the asymptotic iteration method
• Exact Solution of the Klein-Gordon Equation for the PT-Symmetric Generalized Woods-Saxon Potential by the Nikiforov-Uvarov Method
• A note on the Woods-Saxon potential
• Bound States of the Klein-Gordon Equation for Woods-Saxon Potential With Position Dependent Mass

Cited by in corpus (4)

• The generalized Klein-Gordon oscillator in a Cosmic Space-Time with a Space-Like Dislocation and the Aharonov-Bohm Effect
• Scattering of Klein-Gordon particles in the background of mixed scalar-vector generalized symmetric Woods-Saxon potential
• Remarks on the Woods-Saxon Potential
• Matching polynomial tails to the cut-off Woods-Saxon potential