CANONICAL TRANSFORMATIONS AND SPECTRUM GENERATING ALGEBRAS IN THE THEORY OF NUCLEAR COLLECTIVE MOTION

Abstract

Publisher Summary This chapter discusses the canonical transformations and spectrum generating algebras in the theory of nuclear collective motion. The method of canonical transformations provides valuable physical insights into the interpretation of the algebraic cm (3) model and into its relationship with the phenomenological models of quadrupole collective motions. It provides the kinetic energy component of the cm(3) Hamiltonian and observables l 2 and L' 2 that can measure the extent to which a given state describes irrotational or rigid flow. It also raises some fundamental questions regarding the nature of collective motions, namely, the impossibility of pure rigid collective flow and the impossibility of expressing a many-particle wave function in terms of the collective and intrinsic coordinates. All the variables in the kinetic energy are well-defined and have a well-defined action on many-particle Hubert space. However, it does mean that a given wave function, expressed in terms of particle coordinates, cannot be reexpressed in terms of the cm, collective, and intrinsic coordinates.