  We study the particle-hole asymmetry of the scattering rate in strongly
correlated electron systems by examining the cubic $\omega^3$ and $\omega T^2$
terms in the imaginary part of the self-energy of the Anderson impurity model.
We show that the sign is opposite in the weak-coupling and strong-coupling
limits, explaining the differences found in theoretical approaches taking the
respective limits as the starting points. The sign change in fact precisely
delineates the cross-over between the weak and strong correlation regimes of
the model. For weak interaction $U$ the sign reversal occurs for small values
of the doping $\delta=1-n$, while for interaction of order $U \approx 2
\Gamma$, $\Gamma$ being the hybridization strength, the cross-over curve
rapidly shifts to the large-doping range. This curve based on the impurity
dynamics is genuinely different from other cross-over curves defined through
impurity thermodynamic and static properties.
