Migdal's theorem in heavy fermion systems

The problem of non-adiabaticity in strongly correlated electron systems has been a subject of considerable attention. We concentrate on the role of ve rtex corrections to electron-phonon interaction for heavy fermion systems i n the normal state. The range of energy transfer important for heavy fermio n systems is not set by the energy characteristic of phonons (Debye energy) , as in the case of normal metals, but is determined by the characteristic energy scale T* (spin fluctuation temperature). To preserve characteristic features of heavy fermion systems we introduce a very simple model assuming a huge density of states near the Fermi level and a very large electron ef fective mass. We present an estimate of the lowest-order vertex correction to electron-phonon interaction and show that the Migdal's theorem is not va lid for heavy fermion systems. (C) 1999 Elsevier Science B.V. All rights re served.