We propose a new approximation scheme to obtain analytic expressions for the bound state energies and eigenfunctions of Yukawa like potentials. The predicted energies are in excellent agreement with the accurate numerical values reported in the literature.
The − s wave Schrödinger and, to clarify one interesting point encountered in the calculations, Klein-Gordon equations are solved exactly for a single neutron moving in a central WoodsSaxon plus an additional potential that provides a flexibility to construct the surface structure of the related nucleus. The physics behind the solutions and the reliability of the results obtained are discussed carefully with the consideration of other related works in the literature. In addition, the exhaustive analysis of the results reveals the fact that the usual Woods-Saxon potential cannot be solved analytically within the framework of non-relativistic physics, unlike its exactly solvable relativistic consideration.
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