  We investigate the thermalization and the chemical equilibration of a parton
plasma created from Au+Au collision at LHC and RHIC energies starting from the
early moment when the particle momentum distributions in the central region
become for the first time isotropic due to longitudinal cooling. Using the
relaxation time approximation for the collision terms in the Boltzmann
equations for gluons and for quarks and the real collision terms constructed
from the simplest QCD interactions, we show that the collision times have the
right behaviour for equilibration. The magnitude of the quark (antiquark)
collision time remains bigger than the gluon collision time throughout the
lifetime of the plasma so that gluons are equilibrating faster than quarks both
chemically and kinetically. That is we have a two-stage equilibration scenario
as has been pointed out already by Shuryak sometimes ago. Full kinetic
equilibration is however slow and chemical equilibration cannot be completed
before the onset of the deconfinement phase transition assumed to be at
$T_c=200$ MeV. By comparing the collision entropy density rates of the
different processes, we show explicitly that inelastic processes, and
\emph{not} elastic processes as is commonly assumed, are dominant in the
equilibration of the plasma and that gluon branching leads the other processes
in entropy generation. We also show that, within perturbative QCD, processes
with higher power in \alpha_s need not be less important for the purpose of
equilibration than those with lower power. The state of equilibration of the
system has also a role to play. We compare our results with those of the parton
cascade model.
