Algebraic cluster models 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 $SU(1,1)$ Lie algebra within the framework for two-, three- and four- body algebraic cluster models that explains both regions $O(4)\leftrightarrow U(3)$, $O(7)\leftrightarrow U(6)$ and $O(10)\leftrightarrow U(9)$, respectively . We offer that this method can be used to study of $k\alpha +x$ nucleon structures with k = 2, 3,4 and x = 1, 2, . . . , in specific x = 1,2 such as structures ${}^{9}Be$,${}^{9}B$,${}^{10}B$ ; ${}^{13}C$, ${}^{13}N$, ${}^{14}N$; ${}^{17}O$, ${}^{17}F$. Numerical extraction to the energy levels, the expectation value of boson number operator and 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.

arXiv commentarXiv admin note: text overlap with arXiv:1608.07487, arXiv:1412.5552, arXiv:1309.4881 by other authors

References in corpus (10)

• Structure of Light Unstable Nuclei Studied with Antisymmetrized Molecular Dynamics
• Molecular Dynamics for Fermions
• Evidence for Triangular D_3h Symmetry in 12C
• Algebraic Models of Hadron Structure II. Strange Baryons
• Evidence for tetrahedral symmetry in 16O
• The algebraic cluster model. Three-body clusters
• Cluster Structures of the Ground and Excited States of 12Be Studied with Antisymmetrized Molecular Dynamics
• Cluster states in nuclei as representations of a U(n+1) group
• The Algebraic Cluster Model: Structure of 16O
• Spectrum Generating Algebra for X${}_3$ Molecules