Two-step formula for a well-defined intermediate state

3 Two-step formula for a well-defined intermediate state 

As a special application of the two-step model the non-coincident observation of photon-induced Auger electron emission will be considered further. In this case one has to integrate the transition rate P of equ. (8.66a) over dKa, because the photoelectron is not observed, i.e., 

However, because of the integration over all directions of the emitted photoelectron, the cross terms must vanish, and only the diagonal terms remain due to the following symmetry arguments. Within the dipole approximation and for incident linearly polarized light, the convenient quantization axis is the direction of the electric field vector. For randomly oriented atoms in the initial state this electric field vector is then the only direction of preference in the initial system (atom plus photon). Since the observation of the final system (ion, photoelectron and Auger electron) is made only for one constituent (the ejected Auger electron), 

The summations over Mf and ms are needed because no observation is made with respect to these final-state quantum numbers. ka and Kph are the wavenumber vectors of the Auger electron and the photoelectron, the minus sign indicates the correct asymptotic boundary condition for the wavefunctions, Vc is the Coulomb interaction between the electrons causing the Auger transition, and z is the dipole operator causing the photoionization process. 

Finally, the conditions necessary for deriving the given two-step formula for Auger electron emission will be summarized. Equ. (8.66) describes the coincident observation of the Auger electron with its preceding photoelectron for  

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