  We consider tunneling of two interacting atoms with an even spatial symmetry.
The atoms are prepared in two lowest excited states with respect to relative
and center-of-mass motions. We observe monotonic and non-monotonic dependence
of the decay rate of the total probability as a function of the interatomic
coupling strength $g$. We find a transition from uncorrelated to correlated
pair tunneling as a function of $g$ and an external trap barrier. The similar
system has been investigated for two interacting $^6$Li atoms in the
deterministic Heidelberg experiment.
