  We show through a perturbative and an exact calculation using Wilson's
renormalization methods that in the problem of two interacting Kondo
impurities, on-site potential scattering generates a quantum-tunneling between
the two impurities through a marginally relevant operator. The magnitude of
this tunneling $V_{12}$ depends on the spin-correlation between the two
impurities. For exchange interactions between the moments comparable to the
Kondo energy $T_K$, $V_{12}$ is typically much larger than $T_K$. This implies
that the heavy-fermion mass in this interesting range is determined by $V_{12}$
rather than $T_K$. The importance of these results for experiments in coupled
Kondo dots is also pointed out.
