Excitation of autoionising resonances

The study of resonances in chapter 8 involved cross sections for elastic and inelastic scattering that are affected by resonances in the electron—target compound system. A new dimension in the study of resonances and the ionisation mechanism is provided by kinematically-complete experiments that can be considered as the excitation of autoionising resonances of the 

The differential cross section for resonant ionisation has been calculated by McCarthy and Shang (1993). The approximation treats the T-matrix element as a coherent superposition of two amplitudes. One describes direct ionisation and is analogous to the amplitudes of section 10.1. The other contains the momentum kj in a resonant amplitude that has an entirely different structure. One can find values of 9s for which the direct amplitude is small (see fig. 10.1 for an analogous reaction). Here the resonant amplitude dominates the T-matrix element. At angles 6s where the direct amplitude is large, interference between the direct and resonant amplitudes is observed. 

Resonant amplitudes are calculated by scattering methods that are very well understood (section 8.2.5). We can therefore consider the resonant ionisation reaction as an extremely-sensitive test of the approximation used for direct ionisation, since it depends on the magnitude and phase of the direct amplitude. 

The amplitude for resonant ionisation is written in a distorted-wave formalism as 

The distorted wave ip +)(ks)) is calculated in the Coulomb potential U of the electron—ion system. The Schrodinger equation of the ion is 

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