Relationship between the interacting boson model of Arima and Iachello and the collective model of Bohr and Mottelson

The generator coordinate method is used to relate the interacting boson model and the collective model through an isometric transformation. It associated complex parameters to the original boson operators whereas the ultimate collective variables are real. The mapping of operators of the interacting boson model onto those of the collective model turns out to be of Holstein-Primakoff type.     

On the relation between the interacting boson model of Arima and Iachello and the collective model of Bohr and Mottelson. II

The generator coordinate method is used to relate the interacting boson model of Arima and lachello and the collective model of Bohr and Mottelson through an isometric transformation. It associates complex parameters to the original boson operators whereas the ultimate collective variables are real. The absolute squares of the collective wave functions can be given a direct probability interpretation. The lowest order Bohr-Mottelson hamiltonian is obtained in the harmonic approximation to the interacting boson model; unharmonic coupling terms render the collective potential to be velocity dependent. The mapping of operators of the interacting boson model onto those of the Bohr-Mottelson model turns out to be of Holstein-Primakoff type.     

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.     

A study of collective octupole states in barium in the interacting boson model

We analyze low-lying collective negative parity states in ^140–148Ba in terms of the interacting spdf boson model. We point out the crucial role played by p bosons in describing E1 transitions. We discuss the rather unusual properties of the nucleus ¹⁴⁶Ba.     

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.     

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.     

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.     

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.     

Study of Bohr–Mottelson with minimal length effect for Q-deformed modified Eckart potential and Bohr–Mottelson with Q-deformed quantum for three-dimensional harmonic oscillator potential

Bohr–Mottelson Hamiltonian on the γ-rigid regime for Q-deformed modified Eckart and three-dimensional harmonic oscillator potentials in the β-collective shape variable was investigated in the presence of minimal length formalism and Q-deformed of the radial momentum part. By introducing new wave function and using the Q-deformed potential concept in Bohr–Mottelson Hamiltonian in the minimal length formalism, the un-normalized wave function and energy spectra equation were obtained by using the hypergeometric method. Meanwhile, the Bohr–Mottelson Hamiltonian in the presence of the quadratic spatial deformation to the momentum in collective shape variable was investigated using transformation of a new variable such as the Schrodinger-like equation with shape invariant potential. The energy equation and un-normalized wave function were obtained using the hypergeometric method. The results showed that the Bohr–Mottelson equations with different energy potentials and different deformation forms in the radial momentum reduced to the similar Schrodinger-like equation with the modified Poschl–Teller potential.     

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.     

Large boson number IBM calculations and their relationship to the Bohr model

Recently, the SO(5) Clebsch-Gordan (CG) coefficients up to the seniority v _max = 40 were computed in floating point arithmetic (T.A. Welsh, unpublished (2008)); and, in exact arithmetic, as square roots of rational numbers (M.A. Caprio et al., to be published in Comput. Phys. Commun.). It is shown in this paper that extending the QQQ model calculations set up in the work by D.J. Rowe and G. Thiamova (Nucl. Phys. A 760, 59 (2005)) to N = v _max = 40 is sufficient to obtain the IBM results converged to its Bohr contraction limit. This will be done by comparing some important matrix elements in both models, by looking at the seniority decomposition of low-lying states and at the behavior of the energy and B(E2) transition strengths ratios with increasing seniority.     

On the boson mapping of fermion collective pairs

We study the problem of the mapping of fermion collective pairs onto particle-particle bosons and of different fermion operators (hamiltonian, one- and two-particle transfer operators) onto corresponding boson ones and we test the consequences of the truncation to lowest orders of these boson operators. We find that, although the lowest-order terms in the expansion of the operators in boson space lead to matrix elements between boson states which display the qualitative behaviour of the corresponding ones between fermion states, higher-order terms are required to get a quantitative agreement when a large number of particles are involved, as a direct consequence of the increased role of the Pauli principle.     

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.     

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.