  Recent experiments have suggested that the electron-phonon coupling may play
an important role in the $\gamma \rightarrow \alpha$ volume collapse transition
in Cerium. A minimal model for the description of such transition is the
periodic Anderson model. In order to better understand the effect of the
electron-phonon interaction on the volume collapse transition, we study the
periodic Anderson model with coupling between Holstein phonons and electrons in
the conduction band. We find that the electron-phonon coupling enhances the
volume collapse, which is consistent with experiments in Cerium. While we start
with the Kondo Volume Collapse scenario in mind, our results capture some
interesting features of the Mott scenario, such as a gap in the conduction
electron spectra which grows with the effective electron-phonon coupling.
