Electric and dynamic quadrupole moments of even-even nuclei

For the ground-state bands of nonmagic even-even nuclei, the variable moment-of-inertia law defines an effective moment of inertia I (J), using only the energies of the 2/sup +/ and 4/sup +/ states. From the definition, I (J) is never negative. The ''average'' moment of inertia I/sub 0/2 equivalent 1/2(I (0( + I (2)) may then be related to the transition quadrupole moment Q/sub 0/2. I (Q) is well described by a continuous function ranging over almost two orders of magnitude in both quantities. This function is linear for small values of Q (< or approx. = 4 e b), quadratice for intermediate values (4 < or approx. = Q < or approx. = 11 d b), and essentially constant for larger values (11 < or = Q < or = 13 e b). The linear section pertains to all nuclei which deviate by not more than two pairs from being singly magic. In this group are both light deformed nuclei (e.g., /sup 1/2C and /sup 2/4Mg) and heavier spherical nuclei ranging from 30 < or approx. = A < or approx. = 200. The values of I and Q in this region are (within +- 50%) those that would bemore » obtained if the nucleus were replaced by a dumbbell with length equal to the nuclear diameter and an ..cap alpha.. particle at either end. The quadratic relation has a simple interpretation in a picture of the nucleus as a droplet composed of two fluids, a superfluid which does not contribute to the angular momentum, and an inertial or rigidly rotating component which forms a fixed fraction f of the mass density at each point in the nucleus. The fraction f, computed according to a simple rule from the degree of deformation of the droplet, vanishes if the droplet is spherical. The constancy of I at the largest Q values (associated with spontaneously fissioning nuclei) may be due to a slight proton excess at the poles of the nucleus.« less