TL;DR
This paper reviews the analytical solutions of the Woods-Saxon potential in nuclear physics, highlighting its limitations and clarifying that exact solutions are not available for zero angular momentum states.
Contribution
It provides a critical review of the solvability of Woods-Saxon potentials, emphasizing the absence of analytical solutions for l=0 states in lower dimensions.
Findings
Approximate solutions are successful for certain nuclei.
Exact solutions do not exist for l=0 states.
Clarifies misconceptions in the literature.
Abstract
More recently, comprehensive application results of approximate analytical solutions of the Woods-Saxon potential in closed form for the 5-dimensional Bohr Hamiltonian have been appeared [14] and its comparison to the data for many different nuclei has clearly revealed the domains for the sucsess and failure in case of using such potential forms to analyse the data concerning with the nuclear structure of deformed nuclei within the frame of the collective model. Gaining confidence from this work, exact solvability of the Woods-Saxon type potentials in lower dimensions for the bound states having zero angular momentum is carefully reviewed to finalize an ongoing discussion in the related literature and clearly shown that such kind of potentials have no analytical solutions even for l=0 case.
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