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- W2022751508 abstract "The $mathrm{sp}(3,R)$ mean field approximation describes collective nuclear rotation in a symplectic density matrix formalism. The densities are $6ifmmodetimeselsetexttimesfi{}6$ matrices that are defined by the quantum mechanical expectations of the symplectic algebra generators. The 21 generators of the noncompact symplectic algebra $mathrm{sp}(3,R)$ include the mass quadrupole and monopole moments, the kinetic energy, the harmonic oscillator Hamiltonian, and the angular, vibrational, and vortex momenta. The mean field approximation restricts the densities to a coadjoint orbit of the canonical transformation group $mathrm{Sp}(3,R).$ The reduction of a $mathrm{Sp}(3,R)$ coadjoint orbit into orbits of the dynamical symmetry group GCM(3) is proved to be consistent with the reduction of an $mathrm{Sp}(3,R)$ discrete series representation into irreducible representations of GCM(3). This reduction places a strict bound on the range of the Kelvin circulation which is the Casimir of the 15-dimensional subalgebra gcm(3)ensuremath{subset}sp(3,R). The cranked anisotropic oscillator and Riemann ellipsoid model are special cases of symplectic mean field theory. The application of the Riemann model in the even-even heavy deformed region indicates that the character of low energy collective rotational modes depends only on the quadrupole deformation ensuremath{beta}. The energy of the first ${2}^{+}$ state in such isotopes is a simple function of ensuremath{beta}." @default.
- W2022751508 created "2016-06-24" @default.
- W2022751508 creator A5088091167 @default.
- W2022751508 date "2002-06-11" @default.
- W2022751508 modified "2023-10-16" @default.
- W2022751508 title "Sp(3,R)mean field theory" @default.
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- W2022751508 doi "https://doi.org/10.1103/physrevc.65.064321" @default.
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