approach is questionable since the LDA calculations cannot be mapped onto a Heisenberg model and there is a need to introduce further terms in form of biquadratic exchange [@Hirschfeld-review]. It is interesting, that immediately after the discovery of high $T_{c}$ in pnictides the electron-phonon pairing mechanism was rather uncritically discarded. This attitude was exclusively based on the $LDA$ band structure calculations of the electron-phonon coupling constant [@Boeri-Dolgov], which in this approach turns out to be rather small $\lambda<0.2$, thus giving $T_{c}<1$ $K$.

In the past there were only few publications trying to argue that the $EPI$ pairing mechanism is an important (pairing) ingredient in the $Fe$-based superconductors [@Kulic-Dolgov-Drechsler]-[@Kulic-Ginzburg; @Conf-2012]. One of the theoretical arguments for it, may be ilustrated in the case of 2-band superconductivity. In the weak-coupling limit $T_{c}$ is given by $T_{c}=1.2\omega_{c}\exp\{-1/\lambda_{\max}\},$ where $\lambda_{\max}=(\lambda_{11}+\lambda_{22}+\sqrt{(\lambda_{11}-\lambda_{22})^{2}+4\lambda_{12}\lambda_{21}})/2$. In the nesting $SFI$ pairing mechanism one assumes a dominance of the repulsive inter-band pairing ( $\lambda_{12}$,$\lambda_{21}<0$), i.e. $\left\vert \lambda_{12},\lambda_{21}\right\vert
\gg\left\vert \lambda_{11},\lambda_{22}\right\vert $. Since the intra-band pairing depends on $\lambda_{ii}=\lambda_{ii}^{epi}-\mu_{ii}^{\ast}$, where $\lambda_{ii}^{epi}$ is the intra-band $EPI$ coupling constant and $\mu
_{ii}^{\ast}>0$ is an screened intra-band Coulomb repulsion, then in order to maximize $T_{c}$ the intra-band $EPI$ coupling it is wishful that $\lambda_{ii}^{epi}$ at least 