Collective motions in nuclei and the spectrum generating algebras T₅ × SO(3), GL(3,R), and CM(3)

Abstract

Cusson's classical treatment of the collective rotations of a discrete system of N particles is extended to the full quantum mechanical system by means of a straightforward generalization of Villars' canonical transformation. In this manner, Bohr's collective Hamiltonian, with various values for the rotational mass, is microscopically derived. The nature and criteria for the existence of various collective flows in a many-body system are also given. The collective parts of the Hamiltonian are then separately expressed in original particle coordinates and momenta and in this manner the possibility of microscopic calculations for the collective motions is suggested. Finally appropriate microscopic Hamiltonians for the S.G.A.'s T 5 × SO(3), GL(3,R), and CM(3) are determined.