u (3)-Boson Model of Nuclear Collective Motion

Abstract
The u(3)-boson model encompasses both the Elliott su(3) and Bohr-Mottelson collective models. The microscopic foundation of the u(3)-boson model is achieved by showing that it is the liquid (i.e., many nucleon) limit of the microscopic collective sp(3,R) theory. For O16 and Ca40 we construct microscopic vibrational states in the sp(3,R) theory which compare remarkably well with the simpler u(3)-boson prediction.