Auxiliary particle theory of threshold singularities in photoemission and x-ray absorption spectra: Test of a conserving T-matrix approximation

We calculate the exponents of the threshold singularities in the photoemiss ion spectrum of a deep core hole and its x-ray absorption spectrum in the f ramework of a systematic many-body theory of slave bosons and pseudofermion s (for the empty and occupied core level). In this representation, photoemi ssion and x-ray absorption can be understood on the same footing; no distin ction between orthogonality catastrophe and excitonic effects is necessary. We apply the conserving slave particle T-matrix approximation (CTMA), rece ntly developed to describe both Fermi and non-Fermi liquid behavior in syst ems with strong local correlations, to the x-ray problem as a test case. Th e numerical results for both photoemission and x-ray absorption are found t o be in agreement with the exact infrared power law behavior in the weak as well as in the strong coupling regions. We point out a close relation of t he CTMA with the parquet equation approach of Nozieres et al.