Quantum Phase Transition in an Extension of the Interacting Boson Model Based on Dual Algebraic Structure

An extension of the original interacting boson model to the multi-level case including negative parity f-and p-bosons is made. An affinealgebraic approach is applied to solve the multi-level pairing problem numerically via the dual algebraic structure. The duality relation is explicitly used to construct the number-conserving unitary and number-nonconserving quasi-spin algebra, related with the Hamiltonian and the corresponding bases. After fitting to the experimental level energies of even-even ^106-116Cd, several order parameters to signify the shape (phase) transition, such as occupation numbers of the bosons in the ground and a few lowest excited states, the level energy staggering in the (quasi)-γ band, are calculated to demonstrate the shape (phase) transitional behavior of these medium mass transitional nuclei.