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Fermi-edge singularity in the vicinity of the resonant scattering condition

Fermi-edge absorption theory predicting the spectrum, A(ω)\propto ω^{-2δ_0/π+δ^2_0/π^2}, relies on the assumption that scattering phase, δ_0, is frequency-independent. Dependence of δ_0 on ωbecomes crucial near the resonant condition, where the phase changes abruptly by π. In this limit, due to finite time spent by electron on a resonant level, the scattering is dynamic. We incorporate this time delay into the theory, solve the Dyson equation with a modified kernel and find that, near the resonance, A(ω) behaves as ω^{-3/4} |\ln ω|. Resonant scattering off the core hole takes place in 1D and 2D in the presence of an empty subband above the Fermi level; then attraction to hole splits off a resonant level from the bottom of the empty subband. Fermi-edge absorption in the regime when resonant level transforms into a Kondo peak is discussed.