SU(3) mean field Hamiltonian

Abstract

The su(3) mean field approximation describes collective nuclear rotation in a density matrix formalism. The densities ρ = q-i l/2 are 3×3 Hermitian matrices in the su(3) dual space, where q is the expectation of the quadrupole moment and l is the expectation of the angular momentum. The mean field approximation restricts these densities to a level surface of the su(3) Casimirs. Each level surface is a coadjoint orbit of the canonical transformation group SU(3). For each density ρ, the su(3) mean field Hamiltonian h[ρ] is an element of the su(3) Lie algebra. A model su(3) energy functional and the symplectic structure on the coadjoint orbit determine uniquely the su(3) mean field Hamiltonian. The densities in time-dependent su(3) mean field theory obey the dynamical equation i = [h[ρ],ρ] on a coadjoint orbit. The cranked mean field Hamiltonian is hΩ = h + i Ω, where Ω is the angular velocity of the rotating principal axis frame. A rotating equilibrium density in the body-fixed frame is a self-consistent solution to the equation [hΩ[],] = 0.