Forward Electron-Phonon Scattering in Normal and Superconducting States

The sharp forward electron-phonon $(FEP)$ and impurity $(FIS)$ scattering change the normal and superconducting properties significantly. The pseudo-gap like features are present in the density of states for $\omega <\Omega $, where $\Omega $ is the phonon frequency. The superconducting critical temperature $T_c$, due to the $FEP$ pairing, is linear with respect to the electron-phonon coupling constant. The $FIS$ impurities are pair weakening for $s-$ and $d-wave$ pairing.