Approximations towards the Cooper-Zare model

In this single-particle approximation and j/J-coupling scheme one then obtains An2 

If in these expressions one neglects the differences in the fine-structure components 

As a last step towards a simplifying approximation one also might neglect the influence of the fine-structure resolved ion core on the radial integrals and phases. In this case one gets the LS-coupling result from the Cooper-Zare model [CZa69]  

3 Photon-induced Lj-MtM, Auger decay in magnesium described as a one- and a two-step process 

In the following, I -M Auger decay in magnesium induced by linearly polarized photons is chosen as an illustrative example for both descriptions. First, the one-step formulation is presented for Auger electrons observed in coincidence with the preceding photoelectron. In successive approximations the two-step formulation is then derived and finally applied to the non-coincident emission of Auger electrons. 

3 Approximations towards the Cooper-Zare model The formulations so far have been rather general, and in the following they will be reduced to the formulations in the independent-particle approximation. First, the Dy are replaced by Dy which leads to the formulation of a and / in the Jij J-coupling case (see [WWa73]). Because only one electron configuration is present in Dy, such a dipole matrix element can be reduced further into the 

---