# Why do nuclear multipole moments of charge density vary with isotopes?

Why do some isotopes have different quadrupole/octupole moments, when these moments of charge density should be independent of mass?

In atomic physics, we have Hund's rules which tell us whether the next electron added to an atom will fill an $s,p,d,f$ orbital. One consequence of the Wigner-Eckart theorem is that the angular momentum of an object constrains its multipolarity. A spinless object may carry only monopole moment; a spin-half object may carry monopole and dipole moments, but no higher; a spin-one object may carry monopole, dipole, and quadrupole moment; etc. A full shell, whether it's an $s$ shell or an $f$ shell, has spherical symmetry. So for atoms, it's the multipolarity of the partially-filled electron orbitals that determines the multipolarity of the atom.