fact that the mobilty or the conductivity is unaffected by forward scattering (i.e., $\theta \approx 0$ or $\cos
\theta \approx 1$) whereas the single-particle level-broadening ($\Gamma \sim
\hbar/\tau_q$) is sensitive to scattering through all angles. Technically, the ($1-\cos\theta$) factor arises from the impurity scattering induced vertex correction in the 2-particle current-current correlation function representing the electrical conductivity whereas the single-particle scattering rate ($\tau_q^{-1}$) is given essentially by the imaginary part of the impurity scattering induced 1-particle electronic self-energy which does not have any vertex correction in the leading-order impurity scattering strength. The absence (presence) of the vertex correction in $\tau_q^{-1}$ ($\tau_t^{-1}$) makes the relevant scattering rate sensitive (insensitive) to forward scattering, leading to a situation where $\tau_q$ and $\tau_t$ could be very different from each other if forward (or small angle) scattering is particularly important in a system as it would be for long range disorder potential.

This could happen in 3D systems if the scattering potential is strongly spatially asymmetric (or non-spherical) for some reason. It was pointed out [@dassarmaPRB1985] a long time ago and later experimentally verified [@exp11] that such a strongly non-spherically symmetric scattering potential arises naturally in 2D modulation-doped structures from random charged impurities placed very 