$$H_e-ph = \sum_\mathbfk, \mathbfk', \lambda M_\lambda(\mathbfq) , c_\mathbfk'^\dagger c_\mathbfk (a_\mathbfq\lambda + a_-\mathbfq\lambda^\dagger)$$
The net effective interaction is attractive for electrons near the Fermi surface with opposite momenta and spins ($\mathbfk, \uparrow$ and $-\mathbfk, \downarrow$) if: ziman principles of the theory of solids 13
$$\delta E_c(\mathbfr) = E_1 , \nabla \cdot \mathbfu(\mathbfr)$$ $$H_e-ph = \sum_\mathbfk
$$\hbar\omega_ph > |E_\mathbfk - E_F|$$