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The nature of the elemental cerium phases, undergoing an isostructural volumecollapse transition, cannot be understood using conventional solid stateconcepts. Using the combination of density functional theory and dynamicalmean-field theory, we study the magnetic properties of both the $\alpha$ andthe $\gamma$ phases. We compute the magnetic form factor, and show that it isvery close to free ion behavior in both the local moment $\gamma$ phase as wellas the more itinerant $\alpha$ phase, in agreement with neutron scatteringexperiments. In sharp contrast, the dynamic local magnetic susceptibility ofthe two phases is strikingly different. In the $\gamma$ phase, the sharp lowenergy peak due to local moment formation and consequently low Kondotemperature dominates the spectra. In the $\alpha$ phase two broad peaks can beidentified, the first is due to Kondo screening, and the second is due toHund's coupling. This shows that hybridization plays a central role in the$\alpha-\gamma$ transition in cerium, and that from the point of view ofmagnetic properties, the $4f$ electrons are strongly correlated in both phases.

$\alpha-\gamma$ transition in cerium: magnetic form factor and dynamic magnetic susceptibility in dynamical mean-field theory