Phonon-mediated electron attraction
= Phonon-mediated electron attraction
{title2=$V_{\rm eff}$}
For <electron> <energy> transfer $\Delta$ and <phonon> <energy> $\Omega_q=\hbar\omega_q$, the symmetrized pair amplitude is $V_{\rm eff}=2|M_q|^2\Omega_q/(\Delta^2-\Omega_q^2)$. It is attractive for $|\Delta|<\Omega_q$. This interaction is retarded, and screened Coulomb repulsion must also be considered.