  The nature of the elemental cerium phases, undergoing an isostructural volume
collapse transition, cannot be understood using conventional solid state
concepts. Using the combination of density functional theory and dynamical
mean-field theory, we study the magnetic properties of both the $\alpha$ and
the $\gamma$ phases. We compute the magnetic form factor, and show that it is
very close to free ion behavior in both the local moment $\gamma$ phase as well
as the more itinerant $\alpha$ phase, in agreement with neutron scattering
experiments. In sharp contrast, the dynamic local magnetic susceptibility of
the two phases is strikingly different. In the $\gamma$ phase, the sharp low
energy peak due to local moment formation and consequently low Kondo
temperature dominates the spectra. In the $\alpha$ phase two broad peaks can be
identified, the first is due to Kondo screening, and the second is due to
Hund's coupling. This shows that hybridization plays a central role in the
$\alpha-\gamma$ transition in cerium, and that from the point of view of
magnetic properties, the $4f$ electrons are strongly correlated in both phases.
