  We present an analytical study of the D'yakonov-Perel' spin relaxation time
for degenerate electrons in a photo-excited electron-hole liquid in intrinsic
semiconductors exhibiting a spin-split band structure. The D'yakonov-Perel'
spin relaxation of electrons in these materials is controlled by electron-hole
scattering, with small corrections from electron-electron scattering and
virtually none from electron-impurity scattering. We derive simple expressions
(one-dimensional and two-dimensional integrals respectively) for the effective
electron-hole and electron-electron scattering rates which enter the spin
relaxation time calculation. The electron-hole scattering rate is found to be
comparable to the scattering rates from impurities in the electron liquid - a
common model for n-type doped semiconductors. As the density of electron-hole
pairs decreases (within the degenerate regime), a strong enhancement of the
scattering rates and a corresponding slowing down of spin relaxation is
predicted due to exchange and correlation effects in the electron-hole liquid.
In the opposite limit of high density, the original D'yakonov-Perel' model
fails due to decreasing scattering rates and is eventually superseded by free
precession of individual quasiparticle spins.
