# Quadrupole moment of 3- state in 208Pb?

$^{208}$Pb is a spherical nucleus, so its transition to the first 3$^-$ state is an octupole vibration. Why does this state then have an associated quadrupole moment, as mentioned by several authors? E.g. this and this article.

Attaching two more articles, check this one and this one

The ground state of Pb-208 is spherical (with spin-parity $0^+$, and doubly-magic proton and neutron numbers). However there is nothing that says that its excited states must also be spherical. An octupole vibration may include dipole and quadrupole terms.
Edited: in the spirit of this related answer, a "rotational band" of states with spin-parity $\cdots \to 7^- \to 5^- \to 3^-$ could provide evidence of a nonzero moment of inertia (mass quadrupole moment) for whatever configuration of nucleons makes up the $3^-$ state. I haven't checked whether that sequence exists or whether that's the method used in the papers you cite, however.