Cooper-Zare model

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... 

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] ... 

The summation for the coefficient of the P2 term likewise includes phase insensitive contributions where I m = Im, but also now one has terms for which I = I 2, which introduce a partial dependence on relative phase shifts— specifically on the cosine of the relative phase shift. Again, this conclusion has long been recognized for example, by an explicit factor cos(ri j — ri i) in one term of the Cooper-Zare formula for the photoelectron (3 parameter in a central potential model [43]. 

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