  We investigate the electron spin dephasing in the presence of spin phase
recovering by a serried $\pi$-pulse sequence in $n$-type (001) GaAs quantum
wells in a wide range of temperature and density regimes. Our numerical
calculation is based on the kinetic spin Bloch equation approach with all the
relevant scatterings explicitly included. We find that the rephasing pulse
sequence with a long inter-pulse spacing only has a marginal influence on the
spin lifetime in both the strong and weak scattering limits. We show that the
spin lifetime can be significantly increased by reducing the inter-pulse
spacing. More interestingly, we show that the temperature and density
dependences of the spin lifetime in the case of short inter-pulse spacing
coincide with those of the momentum scattering time in the low temperature
regime, where nonmonotonic behaviors can appear. The origin of this feature is
that the scattering under the quick rephasing manipulation mainly performs as
the source of the dephasing channel instead of the key to suppress the
inhomogeneous broadening.
  The contributions of the relevant scattering mechanisms are also discussed.
