  The cerium alpha-gamma phase transition is characterized by means of a
many-body Jastrow-correlated wave function, which minimizes the variational
energy of the first-principles scalar-relativistic Hamiltonian, and includes
correlation effects in a non-perturbative way. Our variational ansatz
accurately reproduces the structural properties of the two phases, and proves
that even at temperature $T=0$K the system undergoes a first order transition,
with ab initio parameters which are seamlessly connected to the ones measured
by experiment at finite $T$. We show that the transition is related to a
complex rearrangement of the electronic structure, with key role played by the
p-f hybridization. The underlying mechanism unveiled by this work can hold in
many Ce-bearing compounds, and more generally in other f-electron systems.
