Electron-phonon coupling and longitudinal sound velocity in heavy fermion systems

Heavy fermion systems show pronounced elastic anomalies at low temperatures below a characteristic temperature T* where quasi-particle bands are formed. To explain these anomalies a microscopic theory of electron-phonon interaction in heavy fermion systems is considered for the Periodic Anderson Model. The volume dependence of the hybridization between the f-electrons and the conduction electrons and of the bare f-electrons gives rise to the electron-phonon interaction. The phonon propagator, the phonon self-energy and the velocity of sound in the normal state are calculated at finite temperature and long wavelength limit of phonons. The effects of the phonon coupling strengths, f-level position and the hybridization on the anomalous temperature dependence of the velocity of sound are investigated. The results are discussed on the basis of the experimental results