Complications

[Himanshu Sharma]

1)Perturbation theory requires you to identify a small correction (perturbation) to a well-defined, solvable system. But
A nucleus of general shape doesn’t have a simple, analytical potential.
Without multipole expansion, the perturbing potential due to the deformed charge distribution of the nucleus remains intractable
2) (1)The truncated expansion is valid when the electron is far from the nucleus and higher moments decay rapidly.
(2)First-order perturbation theory is valid when the perturbation is small and does not strongly mix nearby levels.
(3) Yes it is

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