  Starting from a model of 4f-electron generated quadrupolar densities on a
compressible fcc lattice, the elastic anomalies at the Fm3m -> Pa3 phase
transition are studied by means of analytical theory. The model is taken as
representative for the gamma-alpha phase transition in Ce. The coupling of the
(linear) lattice displacements to the square of the quadrupolar orientational
density fluctuations renormalizes the elastic constants. The condensation of
the quadrupolar densities into the orientationally ordered Pa3 structure is
studied as function of temperature and pressure. Precursor effects of the
transition lead to an anomalous softening of the elastic constant c11 while c44
exhibits no such softening. The theoretical results are in excellent
qualitative agreement with pressure experiments on the elastic constants
(equivalently on sound velocities) at the $gamma-alpha transition in Ce.
Lattice dynamical analogies in theory and striking similarities in experimental
results with the Fm3m -> Pa3 transition in C60 fullerite are discussed.
