Magnetic properties regular approximation

From the above discussion it becomes clear that in order to eliminate the spin-orbit interaction in four-component relativistic calculations of magnetic properties one must delete the quaternion imaginary parts from the regular Fock matrix and not from other quantities appearing in the response function (35). It is also possible to delete all spin interactions from magnetic properties, but this requires the use of the Sternheim approximation [57,73], that is calculating the diamagnetic contribution as an expectation value. 

Since we can regard the regular approximation as a Foldy-Wouthuysen transformation, we should be able to use a similar line of development for the property operators as in chapter 16. There we found that it was relatively easy to deal with the electric perturbations because they appeared as powers of the perturbation operator, with a linear operator at lowest order. The magnetic perturbations, on the other hand, were much more complicated because the transformation involved complicated functions of the momentum, which must be replaced with the expression that includes the vector potential. 

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