Sp(3, R) coadjoint orbit theory

Abstract

The algebraic mean field method is applied to the symplectic Lie algebra sp(3, R) that describes geometrical collective states in atomic nuclei. The expectations of sp(3, R) generators define a symplectic density matrix. The mean field approximation restricts the densities to a manifold that is a coadjoint orbit of the transformation group Sp(3, R) and a level surface of the symplectic Casimir functions. Compared to representation theory, mean field theory is technically simpler, but yields similar predictions for physical properties of collective states. The critical points of the energy functional on a coadjoint orbit surface define rotational bands. The deformation, kinetic energy and Kelvin circulation of principal axis symplectic rotors are determined as a function of the angular momentum. Illustrative applications of coadjoint orbit theory are reported for the yrast rotational bands of a light 20Ne and a heavy 166Er deformed isotope.