Effect of an electron-phonon interaction on the one-electron spectral weight of ad-wave superconductor

We analyze the effects of an electron-phonon interaction on the one-electron spectral weight A(k,ω) of a d_x²-y² superconductor. We study the case of an Einstein phonon mode with various momentum-dependent electron-phonon couplings and compare the structure produced in A(k,ω) with that obtained from coupling to the magnetic π-resonant mode. We find that if the strength of the interactions are adjusted to give the same renormalization at the nodal point, the differences in A(k,ω) are generally small but possibly observable near k=(π,0).