We have calculated the quantum quadrupolar interaction due to charge densit
y fluctuations of localized 4f-electrons in gamma-Ce by taking into account
the angular dependence, the degeneracy of the localized 4f-orbitals and th
e spin-orbit coupling. The calculated crystal field of 4f electronic states
is in good agreement with neutron diffraction measurements. We show that o
rientational ordering of quantum quadrupoles drives a Fm (3) over bar m -->
Pa (3) over bar phase transition at similar to 86 K which we assign with t
he gamma-alpha transformation. In the Pa (3) over bar phase the centers of
mass of the Ce atoms still form a face centered cubic lattice. The theory a
ccounts for the first order character of the transition and for the cubic l
attice contraction which accompanies the transition. The transition tempera
ture increases linearly with pressure. Our approach does not involve Kondo
spin fluctuations as the significant process for the phase transition.