Ov. Danylenko et Ov. Dolgov, Nonadiabatic contribution to the quasiparticle self-energy in systems withstrong electron-phonon interaction - art. no. 094506, PHYS REV B, 6309(9), 2001, pp. 4506
We investigate effects of a nonadiabatic electron-phonon(boson) interaction
on the quasiparticle self-energy in the lowest order in the coupling const
ant. Existing approaches either overestimate or underestimate these effects
because of different approximations for momentum and frequency dependences
of the vertex corrections. The connection between the nonadiabaticity and
a possible instability of the interacting Fermi system is discussed as well
.