# Confused about the anapole (toroidal) moment

I am a bit confused about the existence of the anapole moment. As far as I understand, in order to fully describe a charge-current distribution, one needs, beside the normal electric and magnetic moments, toroidal moments. In the static regime, the lowest order, toroidal dipole moment, is called anapole moment. I can understand so far. Now, if I understand this well, the anapole moment appears when doing the expansion of the vector potential in term of $$1/R$$ i.e. a term of this expansion is associated with the anapole moment. However, in Griffiths and Jackson (these are the 2 books I used), when they derive the multipole exapnsion of the vector potential, they obtain the magnetic dipole, quadrupole and so on, but it doesn't seem to be any term left behind. Actually, as far as I understand, the anapole moment should appear at the same order as the magnetic quadrupole. So, assuming their derivation is general (and I assume it is as they took a random current distribution), where is the anapole moment term hidden? And where are all the other higher order toroidal moments, too? A second thing I am confused about is the fact that the anapole moment seem to produce parity violation in atoms. How can this be possible, as the anapole moment is a QED phenomena and QED doesn't violate parity. Is the weak interaction involved somehow? Thank you!

If you are familiar with what is often called Mie theory (the theory of the field scattered by a sphere illuminated by a planewave), and the expansion of a scattered field onto vector spherical harmonics, the anapole can appear clearly in the $$a_1$$ coefficient (the so called dipolar coefficient) as a sharp dip into an otherwise broad resonance (see Fig. 1 in [1]). Plotting the $$a_1$$ coefficient in the complex frequency plane reveals multiple poles corresponding to the various terms mentioned above (the imaginary part of the frequency being related to the width of the resonance).