Ultrasonic attenuation and the coupling of the heavy fermions to the lattice

An unusual ultrasonic attenuation peak has been found by Müller et al. for the attenuation of longitudinal sound as a function of temperature around 10-12K for UPt3. A theoretical model is proposed here to study the attenuation in the heavy fermion systems in the normal state. The model considers the Periodic Anderson Model in presence of phonon coupling to the hybridization as well as to the bare f-electrons. The phonon Green's function is calculated by Zubarev technique. The temperature dependence of ultrasonic attenuation coefficient is calculated from the imaginary part of the phonon self-energy in the dynamic and long wavelength limit. The ultrasonic attenuation peak is described in terms of a narrow hybridization gap in the density of state above the Fermi surface in the conduction band.