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Register a new userTriaxial rigidity of $^{166}$Er and its Bohr-model realization
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The triaxial nature of low-lying rotational bands of $^{166}$Er is presented from the viewpoint of the Bohr Hamiltonian and from that of many-fermion calculations by the Monte Carlo shell model and the constrained Hartree-Fock method with projections. A recently proposed novel picture of those bands suggests definite triaxial shapes of those bands, in contrast to the traditional view with the prolate ground-state band and the $gamma$-vibrational excited band. Excitation level energies and E2 transitions can be described well by the Bohr Hamiltonian and by the many-fermion approaches, where rather rigid triaxiality plays vital roles, although certain fluctuations occur in shell-model wave functions. Based on the potential energy surfaces with the projections, we show how the triaxial rigidity appears and what the softness of the triaxiality implies. The excitation to the so-called double $gamma$-phonon state is discussed briefly.
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We expand the triaxial projected shell model basis to include triaxially-deformed multi-quasiparticle states. This allows us to study the yrast and gamma-vibrational bands up to high spins for both gamma-soft and well-deformed nuclei. As the first application, a systematic study of the high-spin states in Er-isotopes is performed. The calculated yrast and gamma-bands are compared with the known experimental data, and it is shown that the agreement between theory and experiment is quite satisfactory. The calculation leads to predictions for bands based on one- and two-gamma phonon where current data are still sparse. It is observed that gamma-bands for neutron-deficient isotopes of 156Er and 158Er are close to the yrast band, and further these bands are predicted to be nearly degenerate for high-spin states.
We discuss in depth the application of the classical concepts for interpreting the quantal results from the triaxial rotor core without and with odd-particle. The corresponding limitations caused by the discreteness and finiteness of the angular momentum Hilbert space and the extraction of the relevant features from the complex wave function and distributions of various angular momentum components are discussed in detail. New methods based on spin coherent states and spin squeezed states are introduced. It is demonstrated that the spin coherent state map is a powerful tool to visualize the angular momentum geometry of rotating nuclei. The topological nature of the concepts of transverse and longitudinal wobbling is clarified and the transitional axis-flipregime is analysed for the first time.
Background: Recent accumulation of experimental data is revealing the nuclear deformation in vicinity of 42Si. This requests systematic theoretical studies to clarify more specific aspects of nuclear deformation and its causes. Purpose: The purpose of this study is to investigate the nature and cause of the nuclear deformations and its relation to the loss of the neutron magic number N = 28 in vicinity of 42Si. Method: The framework of antisymmetrized molecular dynamics with Gogny D1S density functional has been applied. The model assumes no spatial symmetry and can describe triaxial deformation. It also incorporates with the configuration mixing by the generator coordinate method. Results: We show that the shell effects and the loss of the magicity induce various nuclear deformations. In particular, the N = 26 and N = 30 isotones have triaxially deformed ground states. We also note that the erosion of the N = 28 magicity gradually occurs and has no definite boundaries. Conclusion: The present calculation predicts various nuclear deformations in vicinity of 42Si and suggests that the inter-band electric transitions are good measure for it. We also remark that the magicity is lost without the single-particle level inversion in the oblate deformed nuclei such as 42Si.
Inspired by the recent experimental data (Phys. Lett. B {bf 675} (2009) 420), we extend the triaxial projected shell model approach to study the $gamma$-band structure in odd-mass nuclei. As a first application of the new development, the $gamma$-vibrational structure of $^{103}$Nb is investigated. It is demonstrated that the model describes the ground-state band and multi-phonon $gamma$-vibrations quite satisfactorily, supporting the interpretation of the data as one of the few experimentally-known examples of simultaneous occurrence of one- and two-$gamma$-phonon vibrational bands. This generalizes the well-known concept of the surface $gamma$-oscillation in deformed nuclei built on the ground-state in even-even systems to $gamma$-bands based on quasiparticle configurations in odd-mass systems.
In addition to shape oscillations, low-energy excitation spectra of deformed nuclei are also influenced by pairing vibrations. The simultaneous description of these collective modes and their coupling has been a long-standing problem in nuclear structure theory. Here we address the problem in terms of self-consistent mean-field calculations of collective deformation energy surfaces, and the framework of the interacting boson approximation. In addition to quadrupole shape vibrations and rotations, the explicit coupling to pairing vibrations is taken into account by a boson-number non-conserving Hamiltonian, specified by a choice of a universal density functional and pairing interaction. An illustrative calculation for $^{128}$Xe and $^{130}$Xe shows the importance of dynamical pairing degrees of freedom, especially for structures built on low-energy $0^+$ excited states, in $gamma$-soft and triaxial nuclei.
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