PHONON RENORMALIZATION AND SYMMETRY OF THE SUPERCONDUCTING ORDER-PARAMETER

We present a method for the calculation of the renormalization of the phonon energy in the superconducting state. The expression is derived in the weak-coupling case and takes into account the k dependency of t he order parameter Delta(k). The phonon shift as well as the linewidth are calculated. The influence of the anisotropy of the gap in the ab plane of the high-T-c superconductors on the renormalization of the q- ->O phonon energies is studied. The anisotropies considered have eithe r s-, d-wave, or mixed character. It is shown that an anisotropic gap with s-wave symmetry leads to a renormalization of the phonon energy b elow T-c that is in agreement with the Raman measurements. The renorma lization resulting from the d-wave case instead is incompatible with t hese experiments. Finally, the strength of the electron-phonon couplin g is estimated for the Raman observed phonons.