INFRARED DIVERGENCE IN PSEUDO-PARTICLE SPECTRA

Infrared divergence in the pseudo-particle spectra of the degenerate i mpurity Anderson model described in terms of the auxiliary particles i s examined rigorously with use of the expansion from the large limit o f the spin-orbital degeneracy N. The results of analysis with the most divergent terms in the expansion confirm the exponents of the spectra of the slave boson and the pseudo-fermion to be given respectively by 1 - n(f)(2)/N and (2n(f) - n(f)(2))/N where n(f) is the average numbe r of localized electrons at the impurity site, rather than by N/(N + 1 ) and 1/(N + 1) as suggested by the results of so-called non-crossing approximation (NCA) studies. In determination of the correct exponents , contributions from the crossing diagrams are crucial. It is also con firmed that all of the infrared divergences in the single particle spe ctra are cancelled out by the corresponding vertex corrections to leav e only non-divergent terms in the scattering rate of the conduction el ectrons.