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چکیده
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The Algebraic Cluster Model(ACM) is an interacting boson model that gives the relative motion of the cluster con gurations in which all vibrational and rotational degrees of freedom are present from the outset. We schemed a solvable extended transitional Hamiltonian based on affine SU(1; 1) Lie algebra within the framework for two-, three- and four- body algebraic cluster models that explains both regions O(4) $ U(3), O(7) $ U(6) and O(10) $ U(9), respectively . We offer that this method can be used to study of k +x nucleon structures with k = 2, 3,4 and x = 1, 2, . . . , in speci c x = 1,2 such as structures 9Be, 9B, 10B; 13C, 13N, 14N; 17O,17F. Numerical extraction to the energy levels, the expectation value of the boson number operator, and the behavior of the overlap of the ground-state wave function within the control parameters of this evaluated Hamiltonian are presented. The effect of the coupling of the odd particle to an even-even boson core is discussed along the shape transition and, in particular, at the critical point.
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