Perturbation theory without multipole expansion

[Jannes]

I think that if you start using perturbation theory for the interaction between nucleus and electron cloud without a multipole expansion you would calculate your unperturbed states only with the nuclear Hamiltonian and the Hamiltonian of the electron cloud without any interaction (the simple Hydrogen-like interaction the monopole term gave is gone). You would not get a wave function that relates the electron cloud and nucleus meaning you can not just continue the quantum mechanical perturbation series. The lowest order of the electron -nuclear interaction Hamiltonian could be added to H_0 but this would not be something easy to solve to get an exact unperturbed state.

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