Comment on `Solution of the Dirac equation for the Woods-Saxon potential with spin and pseudospin symmetry' [J. Y. Guo and Z-Q. Sheng, Phys. Lett. A 338 (2005) 90]

TL;DR

This paper critically examines previous solutions to the Dirac equation with Woods-Saxon potential, clarifies the correct approach, and introduces a new pseudospin-symmetric solution with unique properties.

Contribution

It corrects the earlier method and presents a previously missing pseudospin-symmetric solution with novel features.

Findings

Only the spin-symmetric solution is physically valid among the four

The new pseudospin-symmetric solution exhibits a counterintuitive repulsion-generated property

The corrected method aligns solutions with physical boundary conditions

Abstract

Out of the four bound-state solutions presented in loc. cit., only one (viz., the spin-symmetric one, in the low-mass regime) is shown compatible with the physical boundary conditions. We clarify the problem, correct the method and offer another, "missing" (viz., pseudospin-symmetric) new solution with certain counterintuitive "repulsion-generated" property.