The interacting boson model: Microscopic calculations for the mercury isotopes

Microscopic calculations of the parameters of the proton-neutron interacting boson model (IBM-2) appropriate to the even Hg isotopes are reported. The calculations are based on the Otsuka-Armia-Iachello boson mapping procedure, which is briefly reviewed. Renormalization of the parameters due to exclusion of the l=4 g boson is treated perturbatively. The calculations employ a semi-realistic shell-model Hamiltonian with no adjustable parameters. The calculated parameters of the IBM-2 Hamiltonian are used to generate energy spectra and electromagnetic transition probabilities, which are compared with experimental data and with the result of phenomenological fits. The overall agreement is reasonable with some notable exceptions, which are discussed. Particular attention is focused on the parameters of the Majorana interaction and on the F-spin character of low-lying levels.     

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(CG) coefficients up to the seniority v _max = 40 were computed in floating point arithmetic (T.A. Welsh, unpublished (2008)); and, in exact arithmetic, as square roots of rational numbers (M.A. Caprio et al., to be published in Comput.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.     

HNC variational calculations of boson matter

A simple and reliable numerical technique is given for determining the two-body distribution function which minimizes the HNC energy of boson matter. Numerical results are presented for the neutron matter homework problem and the ⁴He Lennard-Jones potential. The resulting distribution function is found to have proper asymptotic behaviour and yields reasonable binding energies.     

Nuclear structure of ~(76)Ge from proton-neutron interacting boson model calculations

The properties of low-lying states in ~(76)Ge, especially the characteristics of the mixed-symmetry states, have been investigated within the neutron-proton interacting boson model(IBM-2). By considering the relative energy of d proton boson to be different from that of neutron boson, the low-lying positive parity levels and M1, E2 transition strengths have been calculated. The IBM-2 calculated results are in good agreement with the experimental data. Particularly, the mixed-symmetry states have been reproduced quite well. The calculation and systematic analysis demonstrated that the collective character of ~(76)Ge lies closest to the SU~*_(πν)(3),with some possible O_(πν)(6) dynamic symmetry in IBM-2 viewpoint.     

Effective boson number calculations in Mo and Cd isotopes

The effects of the neutron-proton interaction on the low-lying levels of Mo and Cd isotopes have been considered in the frame of the IBA-1 model by taking into account an effective boson number (N _eff). Both an empirical procedure based on previous IBA-2 mixing calculations and theN _p N _n scheme provide comparableN _eff values. Level spectra and electromagnetic transitions are investigated. The results support the idea that IBA-1 calculations with a suitableN _eff can largely simulate IBA-2 mixing calculations, taking advantage of simplicity and a smaller number of parameters.     

M1 transitions in the (sdg) boson model

Using the $\text{1}\text{N}$ expansion technique we derive expressions for β→g, γ→g and γ→γ M1 transitions in a general boson model. The M1 matrix elements in the sdg-boson model are similar in form to those in the neutron-proton IBM. Comparisons are made to some selected M1 data exhibiting collective character.     

Euler-Lagrange equations and hypernetted chain calculations of boson matter

The use of two-body distribution functions which minimize the HNC approximation to the Jackson-Feenberg energy of boson matter is shown to lead to convenient expressions for the calculation of $\text{?g}\text{?ρ}$, pressure and compressibility. Study of the Pandharipande-Bethe energy of boson matter does not reveal a minimum and raises questions regarding the utility of this energy functional.     

Ferromagnetism in a hard-core boson model

The problem of ferromagnetism – associated with a ground state with maximal total spin – is discussed in the framework of a hard-core model, which forbids the occupancy at each site with more than one particle. It is shown that the emergence of ferromagnetism on finite square lattices crucially depends on the statistics of the particles. Fermions (electrons) lead to the well-known instabilities for finite hole densities, whereas for bosons (with spin) ferromagnetism appears to be stable for all hole densities.     

Dyson-type boson mapping and SU(6) boson model

The Dyson-type boson mapping is applied to realistic cases to show that it is a very promising method for describing nuclear collective motion. Eigenvectors are obtained in the corresponding hermitian boson theory from the results of right- and left-hand-side eigenvalue problems in the Dyson boson theory. The numerical results are compared with those of the SU(6) boson model and exact quasiparticle shell-model calculations within the multi-phonon subspace.     

Charged Higgs boson in the economical 3-3-1 model

The SU(3) _C ⊗ SU(3) _L ⊗ U(1) _X gauge model with two Higgs triplets (the economical 3-3-1 model) is presented. The minimal Higgs potential is considered in detail, and new Higgs bosons with the mass proportional to the bilepton mass are predicted. In the effective approximation, the charged Higgs bosons H ₂ ^± are scalar bileptons, while the neutral scalar bosons H ⁰ and H ₁ ⁰ do not carry a lepton number. The couplings of the charged Higgs bosons to leptons and quarks are given. We show that Yukawa couplings of H ₂ ^± to ordinary leptons and quarks are lepton-number violating. The pair production of H ₂ ^± at high-energy e ⁺ e ⁻ colliders with the polarization of the e ⁺, e ⁻ beams is studied in detail. A numerical evaluation shows that, if the Higgs mass is not too heavy, then the reaction can give an observable cross section in future colliders at a high degree of polarization. The reaction e ⁺ e ⁻ → H ₂ ^± W ^∓ is also examined. We show that the production cross sections of H ₂ ^± W ^∓ are very small, much below the pair production of H ₂ ^± , and, therefore, the associated production of H ₂ ^± and W ^∓ is, in general, not expected to lead to easily observable signals in the e ⁺ e ⁻ annihilation. The text was submitted by the authors in English.     

Study of Pt isotopes in the core excited interacting boson model 1

The core exited IBM model was applied to the Pt isotopes. It was found that the energy spectra of the high-spin states as well as those of the low-spin states can be reproduced quite well. Also, it was found that there is a structure transition between ¹⁸⁶Pt and ¹⁸⁸Pt. The B(E2) values of ¹⁸⁴Pt were calculated and compared with recent experimental data. It was found that the general features of the B(E2) values can be reproduced qualitatively. The need of more boson core excitations is also discussed.     

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.     

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.     

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.