The effect of interaction on temperature behavior of the polarization and the anomalous self-energy for hole-doped and electron-doped cuprates

By considering the spin-fermion model that uses spin fluctuations as mechanism for pairing in HTSCs, we calculate the spin susceptibility or the polarization for hole-doped and electron-doped cuprates. For constant gap, we calculate a part of procedure analytically. In momentum dependent gap we presented polarization in term of frequency at zero temperature firstly and then considering discrete frequencies, we investigate the finite temperature case. Also considering a non-linear equation for superconducting gap, the first order approximation of energy gap in terms of momentum and frequency is represented. Finally, using self-consistent Eliashberg equations, we calculate first order self-energy for electron-doped and hole-doped cuprates and the effect of interaction is investigated.