  This paper presents numerical evidence that for quantum systems with chaotic
classical dynamics, the number of scattering resonances near an energy $E$
scales like $\hbar^{-\frac{D(K_E)+1}{2}}$ as $\hbar\to{0}$. Here, $K_E$ denotes
the subset of the classical energy surface $\{H=E\}$ which stays bounded for
all time under the flow generated by the Hamiltonian $H$ and $D(K_E)$ denotes
its fractal dimension. Since the number of bound states in a quantum system
with $n$ degrees of freedom scales like $\hbar^{-n}$, this suggests that the
quantity $\frac{D(K_E)+1}{2}$ represents the effective number of degrees of
freedom in scattering problems.
