Fermi Liquid Theory and the Independent electron Approximation

In the lecture, the argument was made that at T>0K, the scattering rate:

1/tau = A(E1 - Ef)^2 + B(Kb.T)^2, where A, B are T-independent constants.

So the scattering time tau is approximately proportional to T^2. Arguments are made in A&M that the scattering time tau depends on the interaction potential from Thomas Fermi screening: 4.pi.e^2/k_0^2.

Performing quite a rough dimensional analysis on this quantity, they get that:

1/tau ~ (Kb.T)^2 / h-bar.Ef

At room T, tau is of order 10^-10 seconds, which is 4 orders of magnitude longer than the typical scattering due to impurities. This suggests that the e-e interactions do not have a significant effect on the validity of the independent electron approximation.