NONADIABATIC EFFECTS IN PHONON-SPECTRA OF SUPERCONDUCTORS

The nonadiabatic contribution of the electron-phonon interaction to th e phonon self-energy Sigma(q, omega) of superconductors is studied for different values of the phonon momentum q. It is demonstrated that th e long range Coulomb field does not affect the nonadiabatic contributi on of Sigma(q, co). It is shown in the framework of the BCS theory tha t the vertex corrections for q = 0 lead to the appearance of the pole in the phonon self-energy connected with the collective electron excit ations inside the energy gap and can be an essential contribution to n onadiabatic effects. Sigma(q, omega) has the logarithmic singularity n ear omega approximate to 2 Delta for large values of q but the vertex corrections are not important for this case. It is shown that for q = Q, where Q is the nesting vector, the zero order phonon self-energy Si gma(0)(Q, omega) has the square root singularity as well as for q = 0. The vertex corrections lead again to the appearance of the pole in Si gma(Q, omega) which has a strong influence on nonadiabatic effects. Th e results are compared with the recent neutron scattering measurements in borocarbides. (C) 1998 Published by Elsevier Science Ltd.