In nuclear physics, the electric quadrupole moment is an important physical quantity that characterizes the deformation of the nuclear charge distribution. One of the expectations of the shell model for the nucleus is that for closed shells the nuclear charge is spherically symmetric. If a nucleus is not spherically symmetric, it will have a non-zero electric quadrupole moment.
In general, the charge Ze in the nucleus can be approximated as a uniform distribution. Due to the spin, it can also be regarded as an axisymmetric system based on the spin direction. The electric quadrupole moment of the nucleus has only one independent component.So, when Q>0, the nucleus is prolate ellipsoidal; when Q<0, the nucleus is oblate ellipsoidal.
Nuclear quadrupole will affect the hyperfine structure of the atomic spectrum, which can be used to measure the nuclear electric quadrupole moment. Scattering experiment is also an important method of measuring nuclear quadrupole moment.