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We have measured phonon dispersion relations of the high-pressure phase cerium-oC(4) (alpha' phase with the alpha-uranium crystal structure) at 6.5 GPa by using inelastic x-ray scattering. Pronounced phonon anomalies are observed, which are remarkably similar to those of alpha-U. First-principles electronic structure calculations reproduce the anomalies and allow us to identify strong electron-phonon coupling as their origin. At the low-pressure end of its stability range, Ce-oC4 is on the verge of a lattice-dynamical instability and possibly a charge density wave. The superconducting transition temperatures of the fcc, oC4, and mC4 phases of Ce have been calculated, and the superconductivity observed experimentally by Wittig and Probst is attributed to the oC4 phase.
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