the corresponding one in the $BCS$ model; ($\mathbf{4}$) the long-range $EPI-FSP$ pairing potential in real space makes a short-range potential in the momentum space. The latter gives rise to numerous low-laying excitation energy (above the ground-state) of pairs, thus leading to strong internal pair fluctuations which reduce $T_{c0}$. At $T_{c}<T<T_{c0}$ a pseudogap behavior is expected.

The structure of the paper is following: in *Section II* we calculate the $EPI-FSP$ pairing potential as a function of semi-microscopic parameters in the model of a dipolar layer $TiO_{2}$ with vibrations qf the oxygen ions [@Lee-Interfacial-supplement]-[@Johnston1-2]. In *Section III* the self-energy effects, such as replica bands and their intensities at $T=0$, are studied. The critical temperature $T_{c0}$ is calculated in *Section IV* in terms of the semi-microscopic parameters ($\varepsilon
_{\parallel}^{eff}$, $\varepsilon_{\perp}^{eff}$, $q_{eff}$, $h_{0}$, $n_{d}$). The range of of these parameters, for which one has $T_{c0}\sim100$ $K$, is estimated, too. In *Section V* the effect of nonmagnetic impurities on $T_{c0}$ are studied, while the effects of internal fluctuations of Cooper pairs are briefly discussed in *Section VI*. Summary of results are presented in *Section VII*.

$EPI-FSP$ pairing potential due to dipolar oxygen vibrations in the $TiO_{2}$layer
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It is important to point out that in 