Migdal's theorem for paramagnons in the case of an almost full band

Abstract

It is shown that for the case of a nearly full band, such as the d-band in transition metal Pd, the first order vertex corrections can be ignored compared to the bare electron-paramagnon vertex, in analogy to the Migdal's theorem in the electron-phonon problem. This result suggests that the usual procedure for evaluating the fermion self-energy in the paramagnon theory is justified for the case when the band is almost full.