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Building upon earlier work on the relation between the dimensionless interdotchannel conductance g and the fractional Coulomb-blockade peak splitting f fortwo electrostatically equivalent dots, we calculate the leading correction thatresults 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 asparabolic near its peak. We develop a new treatment of the problem for g muchless than 1 that starts from the single-particle eigenstates for the fullcoupled-dot system. The finiteness of the barrier leads to a small upward shiftof the f-versus-g curve at small values of g. The shift is a consequence of thefact that the tunneling matrix elements vary exponentially with the energies ofthe states connected. Therefore, when g is small, it can pay to tunnel tointermediate states with single-particle energies above the barrier height V.The correction to the zero-width behavior does not affect agreement with recentexperimental results but may be important in future experiments.Comment: Title changed from ``Non-universal...'' to ``Corrections to the  universal...'' No other changes. 10 pages, 1 RevTeX file with 2 postscript  figures included using eps

Corrections to the universal behavior of the Coulomb-blockade peak splitting for quantum dots separated by a finite barrier