Sp(3,R) mean field theory for heavy deformed nuclei

Algebraic mean field theory (AMFT) for the symplectic $\mathrm{sp}(3,R)$ algebra is used to derive collective rotational bands in the Riemann ellipsoidal approximation. AMFT is formulated in terms of symplectic density matrices that are defined by the quantum mechanical expectations of the $\mathrm{sp}(3,R)$ operators. The mean field approximation restricts the densities to a coadjoint orbit of the canonical transformation group $\mathrm{Sp}(3,R).$ For principal axis rotation, a system of three algebraic equations is derived from energy minimization on an orbit surface. The system is solved self-consistently for the axis lengths and the potential tensor.

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