The Central Field Approximation Non-Relativistic

Energy level calculations of atomic systems, as well as the wave functions are obtained from the Schrodinger equation  

The non-relativistic Hamiltonian for an idealized system made up of a point nucleus of infinite mass and charge Ze, surrounded by N electrons of mass m and charge - e is  

A better description of the energy level structure of the actinide atoms is obtained by adding to (3) terms of relativistic origin, which, in fact, represent the magnetic interaction of orbital and spin momenta of the electrons. (They are of particular importance for actinides since they depend on the fourth power of the atomic number Z)  

By far the dominant one is the spin-orbit interaction described by a term of the form  

A more accurate description is obtained by including other additional terms in the Hamiltonian. The first group of these additional terms represents the mutual magnetic interactions which are provided by the Breit equation. The second group of additional terms are known as effective interactions and represent, to second order perturbation treatment, interaction with distant configurations . These weak interactions will not be considered here. 

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