The nuclear magnetic dipole moment, μ, is a unique case of a quantum operator describing the nuclear magnetism in terms of the spin of the state the nucleus resides in. Its uniqueness relies on the fact that it is extremely sensitive on the proton-neutron content -and competition- of the wave function. No other observable can really say anything about individual nucleons participating (and how much each of them contributes to) in the wave function. Thus measuring magnetic dipoles moments we can determine the wave function of a nuclear state in terms of the single-particle degrees of freedom.
On the other hand, the electric quadrupole moment, Q, is a quantity that reveals the shape of the nucleus. Most often the nucleus can be a spheroid or an ellipsoid. Ideal spherical nuclei, such as those considered for nuclei with spin/parity 0+, present a zero electric quadrupole moment. If the shape of the nucleus is elongated along the rotation of the axis, similarly to an upside standing rugby ball, Q has a positive value (prolate shape), while in the opposite case of a lay-down egg shaped nucleus (oblate shape) Q is negative. The relationship between the value of the quadrupole moment and the shape of the nucleus is so strong that very often it is only necessary to determine the sign of the quadrupole moment, and not the value itself, to have a nice physics result.
For either type of nuclear moment, several techniques have been developed over the years, with the best known to the wider physics audience being the Nuclear Magnetic Resonance technique (developed by I.I. Rabi who got the Nobel for it in 1944). Lots of experimental data have been accumulated and with the revolution of radioactive beams taking over the nuclear physics community in the past 15 years a new blooming of phenomena is developing fast. Experimental data had been tabulated already since before WWII and more than ten compilations (with some very important ones) have been put together to offer the community a concise way of finding information. However, there has been no online presence of recent data, despite the big efforts by IAEA and other organizations to develop online tools.
Very recently, an effort started 7 years ago in the University of Athens, resulted in the first online -we claim the fullest and most up-to-date- database with nuclear electromagnetic moments. The database was hosted on a private server (http://magneticmoments.info) for a few year and will continue, however, for the time being this URL is redirecting visitors to the IAEA site where the database is currently hosted. The Nuclear Data Section of IAEA has come into an agreement to host the database with a cutoff date Nov 2015 (this means there is no more major update is in the works and appear online by the end of this year).
So, if you are into experimental data, and especially nuclear physics EM moments, stop by and find little treasures. There is also an accompanying blog (http://magneticmoments.info/wp) where fellow researchers can comment, offer valuable insights or even contribute their data.
You are welcome to visit!
PS A related publication was very recently accepted for publication in NIM A. Please, cite it if you are about to use any of the data in the database in your own work doi: 10.1016/j.nima.2015.10.096