The nuclear collective WSp(6,R) model
By including the electric dipole operator among the generators, the sp(6,R) algebra of the nuclear symplectic model is extended to the semidirect sum algebra \(wsp(6,R)=w(3)\rtimes sp(6,R)\), where w(3) is a Heisenberg-Weyl algebra spanned by three pairs of boson creation and annihilation operators and the unit operator. The mathematics of the extended model is studied in detail and techniques are provided to perform numerical applications of the latter. The wsp(6,R) irreducible representations realized in the model are shown to be positive discrete series ones, which can be labelled by their lowest weight. The branching rule and the raising operators for the wsp(6,R)\(\supset sp(6,R)\) chain are obtained. Various bases are constructed in the carrier space of a wsp(6,R) irreducible representation and the corresponding matrix representations of the generators are determined. For this purpose, use is made of a Dyson boson realization of wsp(6,R). Finally, the choice of a physically relevant wsp(6,R) irreducible representation and of a phenomenological collective Hamiltonian in the enveloping algebra of wsp(6,R) is reviewed.
boson creation and annihilation operators
scientific article; zbMATH DE number 4042193
scientific article