The second-order WKB quantization rule is applied to the determination
of the eigenvalues associated with electron thermalization in gases.
It is shown that a few percent error in the WK.B eigenvalues can be re
duced by the second-order correction to less than 0.1% in the case of
the electron thermalization in hard-sphere and helium gases with zero
electric field. A large error of - 116% is drastically reduced to 5% f
or the lowest eigenvalue associated with electron attachment to SF6 in
He. The usefulness of the second-order WKB correction is thus confirm
ed.