Is Axially Asymmetric Nucleus \(\gamma \) Rigid or Unstable?
One of the important consequences of the analyses in Chaps. 4 and 5 concerns the issue of the regularity in the level structure of non-axial (or \(\gamma \) -soft) nuclei. For the past decades, structure of the non-axial nuclei has been studied based on t
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Is Axially Asymmetric Nucleus γ Rigid or Unstable?
6.1 Overview Nuclear shapes reflect deformations of the nuclear surface that arise from collective motion of many nucleons [1]. Ground states of most non-spherical nuclei are characterized by axially-symmetric quadrupole deformations—prolate or oblate. There are, however, also many nuclei in which axial symmetry, i.e., the invariance under the rotation around the symmetry axis of the intrinsic state, is broken in the ground state. The description of axially asymmetric shapes and the resulting triaxial quantum many-body rotors is not restricted to nuclear physics, but has also been developed for other finite quantum systems like polyatomic molecules [2], and hence presents a topic of broad interest. To analyze the variation of ground-state shapes in a sequence of nuclei as, for instance, in an isotopic chain that extends to exotic short-lived isotopes far from stability, it is essential to provide a quantitative microscopic description of deformations characterized by both axial and triaxial mass quadrupole moments. The quadrupole moments can be related to the polar deformation parameters β and γ . The parameter β is proportional to the intrinsic quadrupole moment, and the angular variable γ specifies the type and orientation of the shape. The limit γ = 0 corresponds to axial prolate shapes, whereas the shape is oblate for γ = π/3. Triaxial shapes are associated with intermediate values 0 < γ < π/3. Such shapes have been investigated extensively using theoretical approaches that are essentially based on the rigid-triaxial rotor model of Davydov and Filippov [3] and the γ -unstable rotor model of Wilets and Jean [4]. The former assumes that the collective potential has a stable minimum for a particular value of γ [1], whereas in the latter the potential does not depend on γ and thus the collective wave functions are spread out in the γ direction. However, presumably all known axially-asymmetric nuclei exhibit features that are almost exactly in between these two geometrical limits, characterized by the energy-level pattern of quasi-γ band: relative locations of the odd-spin to the even-spin levels. As the two models originate from different physical pictures, the K. Nomura, Interacting Boson Model from Energy Density Functionals, Springer Theses, DOI: 10.1007/978-4-431-54234-6_6, © Springer Japan 2013
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6 Is Axially Asymmetric Nucleus γ Rigid or Unstable?
question of whether axially-asymmetric nuclei are γ rigid or unstable has attracted considerable theoretical interest [1, 5–8]. In this chapter we address this question from a microscopic perspective, and identifies the appropriate Hamiltonian of the interacting boson model (IBM) [6, 7] for γ -soft nuclei, consistent with the microscopic picture. We thereby provide a solution to the problem concerning the energylevel pattern of the odd-spin states. The most complete and accurate microscopic description of ground-state properties and collective excitations over the whole nuclide chart is presently provide
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