Paper adds a new item to the series of constructions of the
(incomplete) sets of the bound states generated by the Dirac
equation in some elementary central external potential. The idea
is to study just the $s-$wave equations (because then, the
``uncomfortable" centrifugal term vanishes) and to select an
interaction admitting a change of variables which transforms the
equation into the Gauss hypergeometric differential equation.

This time, the authors picked up the special case of the Eckart
potential in the form which has been made popular by R. D. Woods
and D. S. Saxon in Phys. Rev. 95 (1954) 577]. The two different
relativistic versions of this potential with a vector component
$V(r)$ and with a scalar component $S(r)$ are considered,
constrained by a constant shift $C$ in (i) $V=S+C$ (case called
spin-symmetric), (ii) $V=C-S$ (pseudo-spin-symmetric case). Each
of these cases is studied, roughly speaking, (a) at the small $C$
and (b) at the larger $C$.

Summarizing the results of the letter: Two of the proposed
bound-state solutions (i-b) and (ii-a) are simply wrong. It is
easy to show that they manifestly violate the asymptotic physical
boundary conditions. No surprise - they were sought in the
scattering regime.

Bound-state solution (i-a) is correct but not new. The related
text is virtually a carbon copy of the exercise Nr. 64 in S.
Fluegge, Practical Quantum Mechanics I (Springer, Berlin, 1971),
p. 162. By the way, the authors overlooked that this solution is
approximate rather than ``exact" as they claim in the first line
of their Abstract.

Finally, the author's method cannot work in the last contemplated
case (ii-b). Hence, their conclusion (viz., the absence of the
bound-state solutions) remains unfounded. In fact, it may be shown
correct/incorrect for the positive/negative Woods-Saxon couplings,
respectively.


MR2126085 Guo, Jian-You ; Sheng, Zong-Qiang . Solution of the
Dirac equation for the Woods-Saxon potential with spin and
pseudospin symmetry. Phys. Lett. A 338 (2005), no. 2, 90--96.


(2005m:81081)