The final state has a very short life time because of the short life-time of the core hole and the short mean free path of the excited photoelectron with kinetic energy in the range around 20-50 eV . The core hole is filled either via an sum rules are helpful in the interpretation of NEXAFS spectra.
22.
It was based upon the observation that the amplitudes for the s-channel scatterings matched exactly with the amplitudes for the 4-particle amplitude which has the property that it is explicitly s-t crossing symmetric, exhibits duality between the description in terms of Regge poles or of resonances, and provides a closed-form solution to non-linear finite-energy sum rules relating s-and t-channels.
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