Perturbation without multipole expansion

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    I’m not really sure about this. We introduce it first when we are describing the interaction between the electrons and the nucleus. From what I understand we only let the same order of the multipole expansion of each of the two fields interact. So maybe the complications we would run into if we didn’t do that is that we would be describing the interaction of all of the orders of the multipole with all of the orders of the other?

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