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

Fermi-edge absorption theory predicting the spectrum A(ω) ∝ ω(-2δ(0)/π+δ(0)92)/π2) relies on the assumption that scattering phase δ(0) is frequency independent. The dependence of δ(0) on ω becomes crucial near the resonant condition, where the phase changes abruptly by π. In this limit, because of the finite time spent by electron on a resonant level, the scattering is dynamic. We incorporate the finite 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)|lnω|. Scattering off the core hole becomes resonant in 1D and 2D in the presence of an empty subband above the Fermi level; then a deep hole splits off a level from the bottom of this subband. Fermi-edge absorption in the regime when resonant level transforms into a Kondo peak is discussed.