Algebraic cluster model calculations for shape phase transitions of boson-fermion systems

Abstract

The Algebraic Cluster Model (ACM) is an interacting boson model that gives the relative motion of the cluster configurations in which all vibrational and rotational degrees of freedom are present from the outset. We schemed a solvable extended transitional Hamiltonian based on affine [Formula: see text] Lie algebra within the framework for two-, three- and four-body algebraic cluster models that explains both regions [Formula: see text], [Formula: see text] and [Formula: see text], respectively. We offer that this method can be used to study [Formula: see text] nucleon structures with [Formula: see text] and [Formula: see text] in specific [Formula: see text] such as structures [Formula: see text], [Formula: see text], [Formula: see text]; [Formula: see text], [Formula: see text], [Formula: see text]; [Formula: see text], [Formula: see text]. 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.