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1. Not so sure, the potential might not be analytically solvable , whereas supposedly a multipole expansion to every order is exactly solvable.
2.1 The usefullness of the multipole expansion is in cutting it off, if the particular charge distribution at hand is an n+1 pole or doesn’t converge quickly I would think that this limits is usefullness.
2.2 When the perturbating potential is small compared to a ‘main’ one.
2.3 I don’t have a good rigourous, quantitative argument but it might seem plausible to expect that given the small size of nucleus compared to the bohr radius , possible inhomogeneities in the charge distribution of the nucleus might have but a small effect on the potential felt by the electrons, do mountains have a measurable effect on the gravitational potential felt by a satellite ? This might be a case for considering it a perturbation. However the multipole expansion I am not so sure.
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