$\s(T) = \Im\Sigma_p(\iome\rightarrow0)$, reported in . This quantity is related to the scattering rate of the carriers. In a metallic regime $\s(T)$ is expected to vanish at low temperature. While for large doping (right panel) $\s(T)$ vanishes as $T \to 0$ (even if for $\delta = 0.15$ some anomaly is observed at intermediate temperature), the small-doping data clearly confirm the NFL behavior down to very small temperature, even if, strictly at $T=0$ the vanishing $\s$ would be recovered.

Finally, depicts the inverse life-time $\t^{-1}=Z_p \s$ of the doped carriers, where $Z_p^{-1}=1-\Im\Sigma_p(i\o_1)/\p T$. In a Fermi liquid $\t^{-1}$ grows as $T^2\sim \o^2$ at low temperature. Our calculations for small doping show a decay faster than $T^2$ which strengthens the picture of an incoherent metallic state. Once again, a Fermi-liquid behavior is established only at extremely low temperatures if the doping is small, while the large-doping data recover the standard behavior.

The increasing scattering rate as a function of decreasing temperature is usually associated to scattering with impurities[@nflstewart]. In this spirit, in the following we will interpret our results as the scattering of the carriers with fluctuating local moments. This effect can be understood as the results of the competition between the 