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.     

Microscopic foundation of the interacting boson model in thes d-shell nuclei

Starting from an isospin invariant shell-model hamiltonian, we describe a method for deriving microscopically the IBM-hamiltonian appropriate to lights d-shell nuclei. The key ingredients of our approach are:a) the Belyaev-Zelevinsky-Marshalek (BZM) bosonization procedure;b) two successive unitary transformations that extract the “maximally decoupled” collective bosons with angular momentaJ=0(s _ππ ⁺ ,s _νν ⁺ ,s _πν ⁺ ) andJ =2(d _ππ ⁺ ,d _νν ⁺ ,d _πν ⁺ (T=0),d _πν ⁺ (T=1)). The method is applied to obtain the low-energy spectra and the electron scattering form factors for the 0 ₁ ⁺ →2 ₁ ⁺ transitions in²⁰Ne and²⁴Mg. Good agreement with the exact shell-model results is achieved. The inclusion of proton-neutron bosons (s _πν ⁺ ,d _πν ⁺ (T=1),d _πν ⁺ (T=0)), as well as the renormalization of boson parameters due to the non-collective degrees of freedom, are shown to play a crucial role.     

Mean-field derivation of the interacting boson model Hamiltonian and exotic nuclei

A novel way of determining the Hamiltonian of the interacting boson model (IBM) is proposed. Based on the fact that the potential energy surface of the mean-field model, e.g., the Skyrme model, can be simulated by that of the IBM, parameters of the IBM Hamiltonian are obtained. By this method, the multifermion dynamics of surface deformation can be mapped, in a good approximation, onto a boson system. The validity of this process is examined for Sm and Ba isotopes, and an application is presented to an unexplored territory of the nuclear chart, namely, the right lower corner of 208Pb.     

Application of a microscopic interacting boson model to single-closed-shell nuclei

The microscopic treatment of an extended IBM including the pairing vibrational modes is applied to single-closed-shell nuclei with N = 50 or Z = 50. The low-lying spectra in the N = 50 isotones are well described in terms of the quadrupole phonon and the pairing vibration. The Sn isotopes roughly resemble the N = 50 isotones. The behavior of the 0₂⁺, 0₃⁺ and 2₁⁺ levels can be explained fairly well by the present model. Introduction of the pairing-vibrational modes into the IBM is essential for describing the single-closed-shell nuclei.     

Confrontation between the quasiparticle-phonon nuclear model and the interacting boson model for deformed nuclei

TheK ^π=0⁺, 2⁺ and 4⁺ states are considered in doubly even deformed nuclei. It is shown that in the quasiparticle-phonon nuclear model (QPNM) and in the interacting boson model (IBM) a vibrational state has one dominating component. The states withK _n ^π =0 ₃ ⁺ , 0 ₄ ⁺ 0 ₅ ⁺ 2 ₂ ⁺ , 2 ₃ ⁺ , 4 ₁ ⁺ and 4 ₂ ⁺ have a dominating one-phonon component within the QPNM and a two- or three-boson component within the IBM. According to the QPNM the contribution of two-phonon components to the wave functions of these states is less than 10%, i.e. there is a qualitative discrepancy in describing the structure of these states within the QPNM and the IBM. The experimental data indicate the existence in these states of one-phonon or two-quasiparticle components. They are rather well described within the QPNM. These states cannot be described within the IBM. This is due to the fact that the IBM takes into account only a small part of the space of two-quasiparticle states, just the one entering intoΒ- andγ-vibrational states.     

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.     

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.     

Evolution of ground state nuclear shapes in tungsten nuclei in terms of interacting boson model

The tungsten nuclei ^180–190W are investigated within the framework of the interacting boson model using an intrinsic coherent state formalism. The Hamiltonian operator contains only multipole operators of the subalgebra associated with the dynamical symmetries SU(3) and O(6). The study includes the behavior of potential energy surfaces (BES’s) and critical points in the space of the model parameters to declare the geometric character of the tungsten isotopic chain. Some selected energy levels and reduced E2 transition probabilities B(E2) for each nucleus are calculated to adjust the model parameters by using a computer code PH INT and simulated computer fitting programme to fit the experimental data with the IBM calculation by minimizing the root mean square deviations. The ^180–190W isotopes lies in shape transition SU(3)-O(6) region of the IBM such that the lighter isotopes comes very clare to the SU(3) limit, while the behavior ones tend to be near the γ-unstable O(6) limit.     

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.     

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.     

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.     

Level density fluctuations in the generalized interacting boson model

Level density fluctuations are calculated within the generalized interacting boson model proposed for even-even nuclei, in dependence on the truncation parameterk. For the case =2 corresponding to theSU(3) dynamical symmetry of the interacting boson model the fluctuation pattern is close to Poissonian. For cases 2, including the anharmonic vibrator model for which =, a rapid transition to the fluctuation pattern close to GOE is obtained.     

The interacting boson approximation in nuclei with a few valence nucleons

In order to investigate microscopically nuclear collective models, the generator coordinate method as a means for deriving the effective hamiltonian for nuclear collective states is discussed. A simple case is treated as an illustration. Perfect agreement of the result with the exact solution testifies to the adequacy of the method. This method is applied to nuclei with a few valence nucleons and gives us the results of the interacting model in the SU(5) limit. The possibility of application to nuclei with many valence nucleons is also briefly discussed.