  The interaction between an atom moving in a model double-well potential and
the conduction electrons is treated using renormalization group methods in
next-to-leading logarithmic order. A large number of excited states is taken
into account and the Kondo temperature $T_K$ is computed as a function of
barrier parameters. We find that for special parameters $T_K$ can be close to
$1 {\rm K}$ and it can be of the same order of magnitude as the renormalized
splitting $\Delta$. However, in the perturbative regime we always find that
$T_K \alt \Delta $ with a $T_K \alt 1 {\rm K}$ [Aleiner {\em et al.}, Phys.
Rev. Lett. {\bf 86}, 2629 (2001)]. We also find that $\Delta$ remains
unrenormalized at energies above the Debye frequency, $\omega_{\rm Debye}$.
