Approximate eigensolutions of the deformed Woods-Saxon potential via AIM

TL;DR

This paper applies the asymptotic iteration method (AIM) with the Pekeris approximation to solve the Schrödinger equation for the deformed Woods-Saxon potential, deriving energy levels and eigenfunctions in hypergeometric form.

Contribution

It introduces a novel combination of AIM and Pekeris approximation to analytically solve for eigenvalues and eigenfunctions of the deformed Woods-Saxon potential.

Findings

Derived explicit energy levels for the potential

Obtained normalized eigenfunctions in hypergeometric form

Demonstrated the effectiveness of AIM with Pekeris approximation

Abstract

By using the Pekeris approximation, the Schr\"{o}dinger equation is solved for the nuclear deformed Woods-Saxon potential within the framework of the asymptotic iteration method (AIM). The energy levels are worked out and the corresponding normalized eigenfunctions are obtained in terms of hypergeometric function.