quantum multipole expansion

[JRomans]

1)The complication in describing the nucleus + electron quantum system [even with general spherical shape] is in the fact that interaction between electron cloud and nucleus is only addressed in the multipole expansion term of the total hamiltonian (only free nucleus and electron cloud description into one mathematical picture is possible);

2.1)Multipole expansion is valid for a realistic description of a system if the singular parts of the system are coupled and interacting with each other (no more free parts of the system, that are independent from the other systems)
2.2)Including the perturbation theory up to the 1st order in the atomic structure description is valid if one wants to only describe the system up to the atomic energy levels (orbital-spin electron interaction)
2.3)Yes, it is possible as the multipole expansion order directly relates to the perturbation order. The issue that needs to be clarified in the description is the overlap condition between nuclear/electron cloud charge/current distribution

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