  Portnoi and Galbraith recently proposed a beautiful and intriguing
relationship defining the critical screening lengths associated with the
apparition of new bound states for the two-dimensional statically screened
Coulomb potential. Not only does semiclassical quantum theory show that this
relationship is unfortunately not strictly exact, it has also proved helpful in
the search for a potential which exactly verifies Portnoi and Galbraith's
formula, namely $\frac{-e^2}{r (1+r/r_s)^2}$. The analytical eigenfunctions of
the corresponding Schr\"{o}dinger equation at zero energy, when localized, lead
to approximate upper bounds for critical screening lengths of the
two-dimensional statically screened Coulomb potential.
