Definition of Nuclear Quadrupole Moments

Abstract

The quadrupole moment of a nucleus is usually defined1 as “the quantity (3z2 — r2)Av, where the average is taken over the nuclear charges for the state which has the maximum component of spin I in the z direction”. This seems to imply that the average is taken over all the protons in the nucleus; but if this be so, it is impossible to reconcile the measured values of nuclear quadrupole moments quoted by Mattauch2 with current ideas of nuclear size. Thus the quadrupole moment of tantalum is reported to be 6 × 10−24 cm.2, which seems incompatible with a nuclear radius of about 9 × 10−13 cm. It seemed desirable, therefore, to examine carefully the derivation of the measured values.