  The connection between scarring and tunneling in chaotic double-well
potentials is studied in detail through the distribution of level splittings.
The mean level splitting is found to have oscillations as a function of energy,
as expected if scarring plays a role in determining the size of the splittings,
and the spacing between peaks is observed to be periodic of period
{$2\pi\hbar$} in action. Moreover, the size of the oscillations is directly
correlated with the strength of scarring. These results are interpreted within
the theoretical framework of Creagh and Whelan. The semiclassical limit and
finite-{$\hbar$} effects are discussed, and connections are made with reaction
rates and resonance widths in metastable wells.
