User:ANUnuclearhonoursclass/Nuclear Quadrupole Moments

Nuclear Quadrupole Moments
The experimental detection of larger than expected nuclear electric quadrupole moments for a number of nuclei was one piece of evidence that led to the development of deformed shell models such as the Nilsson model. Before it was known that nuclei could be deformed, it was assumed that the only protons that could contribute to the quadrupole moment were those few outside the spherical core (see shell model). In this case, quadrupole moments of up to 0.5 eb (electron barns, 1 eb=$1.602 C.cm^{2}$) are expected. However, quadrupole moments much higher than this have been observed, such as $$^{176}$$Lu which has a measured (ground state) quadrupole moment of around 8.0 eb.

Quadrupole moments can be measured using the molecular beam resonance method. In this method, the atoms are passed through three magnetic fields. The first and last fields possess a gradient, and hence will deflect an atom. The gradients are set to be equal and opposite, so the total deflection will be zero unless the atom has been rotated at some point. Rotation will be detected since changing the direction of the magnetic moment will change the size of the deflection. The rotation itself is done by introducing electromagnetic radiation into the middle, uniform, magnetic field. If the energy of the radiation corresponds to the energy difference between two different projections of the atom's magnetic moment onto the magnetic field direction, the state of the atom can be transferred between these projections.

By observing the frequency of electromagnetic radiation at which the atom is deflected, the molecule's magnetic moment can be determined. In addition, states differing in energy due to a reason other than magnetic moment projection can be distinguished, provided the frequency resolution is sufficiently fine. An example of this is energy differences due to interaction between electrons in an atom and the nuclear electric quadrupole moment .

James Rainwater showed that the large observed moments could be explained if the entire nucleus was deformed, so that all nucleons contribute to the quadrupole moment. In this case, the 71 protons in Lu (for instance) could easily account for the large observed electric quadrupole moment.

The values of nuclear quadrupole moments, Q, can be determined using quadrupole coupling constants, eqQ/h, from atomic, molecular, or solid-state spectroscopy, combined with accurate calculations of the  electric field gradient, q. Another way is to use eqQ/h for muonic atoms. The latest, 'Year 2008' table of values is available in ref. .