Problem without multipole expansion

[Johanna Waltenspiel]

The problem that I could see ocurring would be that the interaction term itself is not small enough to be treated with perturbation theory. Namely the monopole part of this interaction is of the same order of magnitude as atomic energy levels.
We can therefore not view the interaction term as a “small” perturbation.
It is the expansion that allows us to consider the terms of higher order than the monopole which are of a much smaller order of magnitude.

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