Symmetries of the interacting boson model

This contribution reviews the symmetry properties of the interacting boson model of Arima and Iachello. While the concept of a dynamical symmetry is by now a familiar one, this is not necessarily so for the extended notions of partial dynamical symmetry and quasi dynamical symmetry, which can be beautifully illustrated in the context of the interacting boson model. The main conclusion of the analysis is that dynamical symmetries are scarce while their partial and quasi extensions are ubiquitous.     

g-boson excitations in the interacting boson model

We have extended the interacting boson model (IBM) by including the g-boson degree of freedom. Schematic model calculations have been carried out in the two different limits: SU(5) and O(6). Particular applications have been carried out for ¹⁰⁴Ru, a nucleus intermediate between SU(5) and O(6). In all cases, energy spectra, E2 and E4 transition rates have been studied in detail and compared with the most recent experimental data for ¹⁰⁴Ru.     

Electron scattering in the interacting boson model

It is suggested that the interacting boson model be used in the analysis of electron scattering data. Qualitative features of the expected behavior of the inelastic excitation of some 2⁺ states in the transitional SmNd region are discussed.     

Order and chaos in the interacting boson model

We investigate both quantum and classical signatures of order/chaos interplay within the symmetry triangle of the interacting boson model. Special attention is devoted to the increased regularity in the Alhassid-Whelan semiregular arc inside the symmetry triangle. Significant changes in properties of classical trajectories therein are found to accompany the strong bunching of levels in the 0⁺ spectrum. The text was submitted by the authors in English.     

Mixed-symmetry states in the neutron-proton interacting boson model

States of mixed proton-neutron symmetry are investigated in different dynamical symmetries of the interacting boson model. We discuss in each of the limits the energy spectrum, the wave functions and the B(M1; 0₁⁺ → 1 _1⁺) values. We also study three classes of transitional nuclei namely the Pd nuclei [U(5) → O(6)], the Sm nuclei [U(5) → SU(3)] and the Pt nuclei [O(6) → SU(3)] with respect to the energy of the lowest non-symmetric J^π = 1⁺, 3⁺ levels as well as the M1 and M3 strengths for exciting these levels from the ground state. For ⁹⁸Pd we compare this calculation with a shell-model calculation. Finally, we adress the problem of the mixing of the non-symmetric J^π = 1⁺ state with nearby hexadecapole (g-boson) configurations.     

Intrinsic states in the sdg interacting boson model

We give the intrinsic states explicitly in the boson representation in the framework of the sdg interacting boson model. Although they are only valid in the large-N limit, they are useful to estimate various physical quantities in well deformed nuclei. One can compare these results with those predicted in the IBM1 or in the IBM2.     

Phase diagram of the proton-neutron interacting boson model

We study the phase diagram of the proton-neutron interacting boson model with special emphasis on the phase transitions leading to triaxial phases. The existence of a new critical point between spherical and triaxial shapes is reported.     

The moment of inertia in the interacting boson model

We perform a self-consistent cranking calculation of intrinsic states of IBM-1 and IBM-2 for three reasons: (a) to study the effect of Coriolis and centrifugal forces in the IBM; (b) to derive approximate analytic formulae for the energy in some cases where the IBM hamiltonian does not have dynamical symmetry; (c) to study the dependence of the moments of inertia on the variables of the intrinsic IBM states. Choosing a coordinate system where the quadrupole tensor is diagonal reduces the number of variables considerably. Among other applications of our formalism we study the transition between the symmetries SU(3) and SU¹(3) in the IBM-2 hamiltonian H = −(Q_π + Q_ν) · (Q_π + Q_ν). We find that the moments of inertia and the asymmetry variables show a kind of phase transition, as a function of the parameter χ_ν occurring in Q_ν.     

Geometric shapes withg- bosons in the interacting boson model

Geometric aspects of the extended interacting boson model (gIBM) withs, d andg bosons are studied using coherent states. Algebraic expressions for the coherent state expectation values of various terms in the general gIBM Hamiltonian are derived in terms of the quadrupole and hexadecupole deformation variablesβ ₂ andβ ₄ and the asymmetry angleγ. These in turn are used to determine the equilibrium shape parameters (β ₂ ⁰ ,β ₄ ⁰ ,γ ⁰) in the seven dynamical symmetry limits of gIBM.     

Generalized interacting boson model and the collective behaviour in nuclei

The effect of including the high spin bosons on the manifestation of collective behaviour in nuclei is examined by plotting theB(E2; 2⁺→0⁺) rates as a function of neutron number for various values ofη, whereη is the highest angular momentum of the bosons included in the calculation.B(E2; 2⁺→0⁺) values of a large number of nuclei in various regions of the nuclear periodic table are calculated with a single value for the effective charge in the generalized scheme. Irreducible representations of SU(3) contained in the symmetric partition [N] of U(15) are worked out for integersN uptoN=15, to enable the explicit inclusion of theg boson into calculations. The experimentally observed odd-K bands in²³⁴U and¹⁸⁴W are described as a direct consequence of theg boson.     

Vibrations and rotations for the proton-neutron interacting boson model

The interacting proton-neutron boson model (IBM-2) is analyzed in terms of the concepts of a geometrical picture. The centre of mass and relative-motion deformations are determined, and for the deformed systems, rotational and vibrational modes are identified. The parameters in an intrinsic hamiltonian which govern these modes are calculated. For the SU(3) dynamical symmetry a one-to-one mapping is given between low-lying basis states in the geometrical and the algebraic model. The magnetic dipole operator in the geometrical model is derived from its counterpart in IBM-2. This serves as an example for the calculation of static and transition operators, generally.