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At this moment, we used first order pertubation theory. This, however, is only valid when the general shape is more or less spherical (or- cilindrical). Obsviously, this need not to be. Also, we assumed in our laplace expansion that r_n < r_e i.e. the electron cloud is not close to the nucleus, which isn’t valid for a general nucleus.
In general, your results wouldn’t be valid.
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