  Building upon earlier work on the relation between the dimensionless interdot
channel conductance g and the fractional Coulomb-blockade peak splitting f for
two electrostatically equivalent dots, we calculate the leading correction that
results from an interdot tunneling barrier that is not a delta-function but,
rather, has a finite height V and a nonzero width xi and can be approximated as
parabolic near its peak. We develop a new treatment of the problem for g much
less than 1 that starts from the single-particle eigenstates for the full
coupled-dot system. The finiteness of the barrier leads to a small upward shift
of the f-versus-g curve at small values of g. The shift is a consequence of the
fact that the tunneling matrix elements vary exponentially with the energies of
the states connected. Therefore, when g is small, it can pay to tunnel to
intermediate states with single-particle energies above the barrier height V.
The correction to the zero-width behavior does not affect agreement with recent
experimental results but may be important in future experiments.
