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 crossover 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 approximate to 2 Gamma, Gamma being the hybridization strength, the crossover curve rapidly shifts to the large-doping range. This curve, based on the impurity dynamics, is genuinely different from other crossover curves defined through impurity thermodynamic and static properties.