New Approach to Collective Nuclear Motions

Abstract

The use of the elements of the mass quadrupole tensor as generalized, nonredundant variables to describe nuclear collective motions is developed. The Hamiltonian for a group of $n$ identical particles in an oscillator well, which interact with each other by way of quadrupole two-body interactions, is rewritten in terms of the eigenvalues of the mass quadrupole tensor and angular momentum operators. The total angular momentum is separated into a part associated with rotations of the mass quadrupole tensor, and an intrinsic part. A semiclassical argument shows that the energies of states are approximately described by an expression in some respects indistinguishable from that of the empirical variable-moment-of-inertia model, which has been found adequate to represent the energies of the levels of a wide range of even nuclei.