We compare the magnitudes of the single-particle relaxation time exactly computed in the variable phase approach with those computed in the first Born approximation for doped semiconductors such as Si and GaAs, assuming that the Coulomb impurities are randomly distributed centers. We find that for typical dopant concentrations in Si, the Born approximation can overestimate the single-particle relaxation time by roughly 40% and underestimate it by roughly 30%. Finally, we show that the strong interference of phase shifts is missing in the strong scattering regime where the Born approximation fails.

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