General formulation as a one-step process

1 General formulation as a one-step process The interaction of a photon with a magnesium atom can lead to the emission of two electrons with wavenumbers Ka and Kb, provided the photon energy is larger than the threshold energy E,+ + for double photoionization (E,+ + = 22.68 eV for the ejection of the two outer 3s-electrons). Energy conservation then requires 

For a correct treatment of Auger electron emission as a resonance in the double ionization continuum, one has to start with the transition rate P  

In equ. (8.51) the summation over the magnetic quantum numbers takes care of the unobserved substates, and the -function ensures energy conservation. The essential part which is of interest in the present context is the transition matrix element rfi(icams , KbmSb ha) whose dependence on the wavevectors Ka and Kb of the emitted electrons with spin projections mSa and mSb and on the photon energy hot is indicated explicitly. Following the detailed discussion in [TAA87] this matrix 

Several approximations are necessary in making the general one-step formula more tractable for applications to specific aspects and, in particular, to simple cases where the two-step formulation can be applied. Again the example of Auger decay will considered, and the discussion will closely follow the detailed treatment in [TAA87]. 

As a first approximation, direct double photoionization will be neglected. This is often justified because the cross section for double photoionization in outer shells, and hence also the corresponding amplitude, is much smaller than the cross section for single photoionization in an inner shell. Therefore, the Auger decay has 

---