RADIATIVE-CORRECTIONS TO THE LONG-WAVELENGTH OPTICAL-MODE SPECTRUM OFTHE ELECTRON-PHONON MODEL - ABSENCE OF MODE-SPLITTING EFFECTS AND HARDENING OF THE MODE

Renormalization of the phonon spectrum of the Einstein form due to a w eak coupling with electrons is calculated. No splitting of the phonon mode is found. A q-dependent hardening of the long-wave optical phonon s contrasts with the softening of acoustic phonons in a weakly coupled electron-phonon system and with the softening of all phonons in the s trong-coupling polaronic regime.