Electric Quadrupole Moments of Nuclei

The nuclear electric quadrupole moment is a parameter which describes the effective shape of the ellipsoid of nuclear charge distribution. A non-zero quadrupole moment Q indicates that the charge distribution is not spherically symmetric. By convention, the value of Q is taken to be positive if the ellipsoid is prolate and negative if it is oblate.

The quantity Q₀ is the classical form of the calculation represents the departure from spherical symmetry in the rest frame of the nucleus. The expression for Q is the quantum mechanical form which takes takes into account the nuclear spin I and the projection K in the z-direction.

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, so the measurement of the quadrupole moment is a test of the shell theory. Since the quadupole moment depends upon the size and charge of the nucleus, a better comparison is obtained by normalizing for those factors, giving what is called a "reduced quadrupole moment". A plot of measured values shows that magic numbers of neutrons or protons correlate with near-zero quadrupole moments.

Electric quadrupole moments of nuclei can be measured brom hyperfine splitting of atomic spectral lines, from quadrupole hyperfine splitting of molecular rotational spectra, and other spectroscopic techniques.