  The explicit semiclassical treatment of the logarithmic perturbation theory
for the bound-state problem of the radial Shrodinger equation with the screened
Coulomb potential is developed. Based upon h-expansions and new quantization
conditions a novel procedure for deriving perturbation expansions is offered.
Avoiding disadvantages of the standard approach, new handy recursion formulae
with the same simple form both for ground and excited states have been
obtained.
