Perturbation theory without multipole expansion

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    When describing a nuclei system, we use the perturbation theory to add an extra term to the Hamiltonian that describes the interaction between electron and nuclei (charge-charge and current-current interaction). This term is mathematically quite tricky to treat for nucleus with complicated shape, so a good tool to deal with it is doing a multipole expansion.

    So if we start developing all the mathematics for the general case without doing a multipole expansion first, at the moment we will want to study a special shape nuclei we will get stuck, and if we want to continue we will have to eliminate/despise some terms, leading to a bad description of the system, without taking into account all the interactions between electron and nuclei.

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