Exactly solvable model of transitional nuclei based on dual algebraic structure for the three level pairing model in the framework of sdg interacting boson model

In this paper, a successful algebraic method based on the dual algebraic structure for three level pairing model in the framework of sdg IBM is proposed for transitional nuclei which show transitional behavior from spherical to gamma-unstable quantum shape phase transition. In this method complicated sdg Hamiltonian, which is a three level pairing Hamiltonian is determined easily via the exactly solvable method. This description provides a better interpretation of some observables such as BE(4) in nuclei which exhibits the necessity of inclusion of g boson in the sd IBM, while BE(4) cannot be explained in the sd boson model. Some observables such as Energy levels, BE(2), BE(4), the two neutron separation energies signature splitting of the γ-vibrational band and expectation values of the g-boson number operator are calculated and examined for Pd46104−110 isotopes.