Fermi-Edge Singularity in the Vicinity of the Resonant Scattering Condition

Fermi-edge absorption theory predicting the spectrum A(omega) infinity omega(-2 delta 0/pi+delta 02/pi 2) relies on the assumption that scattering phase delta(0) is frequency independent. The dependence of delta(0) on omega becomes crucial near the resonant condition, where the phase changes abruptly by pi. 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(omega) behaves as omega(-3/4) vertical bar ln omega vertical bar. 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.