Picture change effects in approximate relativistic theories

2 Picture change effects in approximate relativistic theories 

The most rigorous way of incorporating relativity in the calculations is achieved by using four-component methods. However, for many applications a full Dirac-Hartree-Fock treatment is not feasible and reduced schemes are preferred keeping the numerical effort much lower. We 

In order to obtain the characteristics of the model one starts from the general expression for the electrostatic interaction energy of two charge distributions 

By the usual multipole expansion of the reciprocal distance at the position To of the nucleus under consideration one obtains the individual 

If one treats the nucleus under consideration as a point charge for the moment the modified interaction energy (50) including the point quadrupole charges now takes the form 

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