  We study the effect of charged impurity screening on spin decoherence in bulk
{\it n}-type GaAs, and analyse in details the effect of the use of different
Born approximations applied to a linearized Thomas-Fermi screening theory. The
spin relaxation times are calculated by ensemble Monte Carlo techniques,
including electron-electron, electron-impurities, and electron-phonons
scattering. We carefully choose a parameter region so that all the physical
approximations hold, and, in particular, a Yukawa-type potential can be used to
describe the screened Coulomb interaction and the Born series converges. Our
results show that including the second order Born approximation yields much
shorter spin relaxation times compared to the commonly implemented first Born
approximation: spin relaxation times may be reduced by hundreds of picoseconds,
with the first Born approximation overestimating results by 30% or more for a
large region of parameters. Though our ensemble Monte Carlo simulations include
electron-electron and electron-phonon interactions, when considering low to
intermediate carrier densities and $T > 50 $ $\mathrm{K}$, but $T$ smaller than
the Fermi temperature, our results are in good agreement with Dyakonov-Perel
theory when this includes electron-impurity interactions only, which supports
this to be the most relevant scattering mechanism for bulk GaAs in this
low-intermediate temperature regime.
