I would do a calculation for an electric dipole first. Please excuse me for
being too lazy to actually do it or to look it up. I expect some radiation
is emitted but probably gets very small when multipoles are considered. In
reality you would have to consider nuclei with dispersed electron clouds. I
guess there is a general proof somewhere?
This is my second year as a high school teacher. When I was doing my Ph.D.
I would at least try such problems, even if I didn't get them solved. Maybe
I need a kick.