over the charge distribution and the potential within a domain : One can write the potential as a Taylor-expansion at the center of the considered nucleus. This method corresponds to the multipole expansion in cartesian coordinates (note that the equations below use the Einstein sum-convention): The first term involving will not be relevant and can therefore be omitted. Since nuclei do not have an electric dipole moment , which would interact with the electric field , the first derivatives can also be neglected. One is therefore left with all nine combinations of second derivatives. However if one deals with a homogeneous oblate or prolate nucleus the matrix will be diagonal and elements with vanish. This leads to a simplification because the equation for the potential energy now contains only the second derivatives in respect to the same variable: The remaining terms in the integral are related to the charge distribution and hence the quadrupole moment. The formula can be simplified even further by introducing the electric field gradient , choosing the z-axis as the one with the maximal principal component and using the Laplace equation to obtain the proportionality written above. For an nucleus one obtains with the frequency-energy relation : Applications There are several research groups around the world currently working on ways to use NQR to detect explosives. Units designed to detect landmines and explosives concealed in luggage have been tested. A detection system consists of a radio frequency (RF) power source, a coil to produce the magnetic excitation field and a detector circuit which monitors for a RF NQR response coming from the explosive component of the object. A fake device known as the ADE 651 claimed to exploit NQR to detect explosives but in fact could do no such thing. Nonetheless, the device was successfully sold for millions to dozens of countries, including the government of Iraq. Another practical use for NQR is measuring the water/gas/oil coming out of an oil well in realtime. This particular technique allows local or remote monitoring of the extraction process, calculation of the well's remaining capacity and the water/detergents ratio the input pump must send to efficiently extract oil. Due to the strong temperature dependence of the NQR frequency, it can be used as a precise temperature sensor with resolution on the order of 10−4 °C. References Nuclear magnetic resonance