Abstract
A simple systematic procedure to construct the proton-neutron unitary, usdπν(12), orthogonal, osdπν(12), and quasi-spin susdπν(1,1) algebras of the sd bosonic system is presented. New algebraic substructures of these algebras are discussed and the explicit formulae for their generators and Casimir operators are given in the spherical tensor form. The complementarity relationship of the Casimir operators of the susdπν(1,1) and osdπν(12) is derived. The exact algebraic solutions of the quantum phase transition Hamiltonian between the osdπν(12) and usπν(2)⊗udπν(10) limits have been considered, for the first time, in the framework of affine susdπν(1,1) Lie algebra. The low lying energy spectra of the 70Ge, 76−78Se, 96−98Mo, and 100−102Ru isotopes are calculated using the osdπν(12)↔usπν(2)⊗udπν(10) transition Hamiltonian. The good agreement of our computation with empirical result in these isotopes emphasizes the importance of usπν(2)⊗udπν(10) limit. With this addition, symmetry can be extended to many nuclei.
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