(as well as in$1ML$ $FeSe/TiO_{2}$) might be an important test for the $EPI-FSP$ pairing in this material.

Finally, it is worth of mentioning, that the real isotope effect in $T_{c0}$ of $1ML$ $FeSe/SrTiO_{3}$ (and in $1ML$ $FeSe/TiO_{2}$) might depend on the type of non-magnetic impurities. If their potential is also long-ranged (for instance due to oxygen deffects in the $TiO_{2}$ dipole layer), then there is $FSP$ in the scattering potential, i.e. $u_{imp}^{2}(q)\approx u^{2}\delta(\mathbf{q})$. Then, such impurities affect in the same way $s$- and $d$-wave pairing and they are pair weakening, as shown in [@Dan-Dol-Kul-Oud]. Naimly, one has $(a)$ $T_{c}^{(s,d)}\approx
T_{c0}[1-4\Gamma_{F}/49T_{c0}]$ for $\Gamma_{F}\ll\pi T_{c}$, where $\Gamma_{F}=\sqrt{n_{i}}u$; (b) $T_{c}^{(s,d)}\approx0.88$ $\Omega\exp
(-\pi\Gamma_{F}/4T_{c0})$, for $\Gamma_{F}\gg\pi T_{c}$. There are two important results: $(1)$ There is a nonanalicity in $\Gamma_{F}\sim\sqrt
{n_{i}}$; $(2)$ there is a full isotope effect in the “dirty” limit $\Gamma_{F}\gg\pi T_{c}$, i.e. $\alpha_{O}=1/2$, since $T_{c}^{(s,d)}\sim\Omega\sim M^{-1/2}$. We stress, that if the full isotope effect would be realized experimentally in $1ML$ $FeSe/SrTiO_{3}$ (and in $1ML$ $FeSe/TiO_{2}$), then this does not automatically exclude the $FSP-EPI$ mechanism of pairing, since it may be due to impurity effects. In that case the nonanalicity of $\Gamma_{F}$ in $n_{i}$ might be a smoking-gun effect.

Internal pair fluctuations reduce $T_{c0}$
