Sdg Interacting Boson Model Research Articles

Exactly solvable model of transitional nuclei based on dual algebraic structure for the three level pairing model in the framework of sdg interacting boson model

In this paper, a successful algebraic method based on the dual algebraic structure for three level pairing model in the framework of sdg IBM is proposed for transitional nuclei which show transitional behavior from spherical to gamma-unstable quantum shape phase transition. In this method complicated sdg Hamiltonian, which is a three level pairing Hamiltonian is determined easily via the exactly solvable method. This description provides a better interpretation of some observables such as BE(4) in nuclei which exhibits the necessity of inclusion of g boson in the sd IBM, while BE(4) cannot be explained in the sd boson model. Some observables such as Energy levels, BE(2), BE(4), the two neutron separation energies signature splitting of the γ-vibrational band and expectation values of the g-boson number operator are calculated and examined for Pd46104−110 isotopes.

Phase transitions in the sdg interacting boson model

A geometric analysis of the sdg interacting boson model is performed. A coherent state is used in terms of three types of deformation: axial quadrupole ( β 2 ), axial hexadecapole ( β 4 ) and triaxial ( γ 2 ). The phase-transitional structure is established for a schematic sdg Hamiltonian which is intermediate between four dynamical symmetries of U ( 15 ) , namely the spherical U ( 5 ) ⊗ U ( 9 ) , the (prolate and oblate) deformed SU ± ( 3 ) and the γ 2 -soft SO ( 15 ) limits. For realistic choices of the Hamiltonian parameters the resulting phase diagram has properties close to what is obtained in the sd version of the model and, in particular, no transition towards a stable triaxial shape is found.

Configuration mixing in the sdg interacting boson model

A wavefunction analysis of the strong-coupling limits of the sdg interacting boson model is presented. The analysis is carried out for two-boson states and allows us to characterize the boson configuration mixing in the different limits. Based on these results and those of a shell-model analysis of the sdg IBM, qualitative conclusions are drawn about the range of applicability of each limit.

Enhancement of B(E2) Collectivity in the sdg-Interacting Boson Model**The project supported by The Science Fund of China Nuclear Industry under grant No. J95AY5021, National Natural Science Foundation of China under grant No. 19775026, Excellent Young University Teachers Fund of National Education Committee of China

It is pointed out that the difficulty in boson models in explaining the large B(E2) experimental data is not due to the lack of collectivity in boson model wavefunction. This long standing problem of reduction in collectivity of wavefunction in boson models can be solved by choosing an appropriate E2 transition operator in the SU(3) limit of the sdg-interacting boson model. The ratio B(E2, L + 2 → L) / B(E2, 2 → 0) can be almost any large number.

Generalized Michailov plot analysis of inband E2 transitions of deformed nuclei

Intraband E2 transitions of some 30 deformed nuclei are analysed using a generalized Michailov plot, based on an E2 transition formula in the SU(3) limit of the sdg interacting boson model. The general E2 transition formula in the sdg-IBM has an term in addition to the usual SU(3) model result. It is found that the general E2 formula can describe the inband transitions well. Comparisons with other models are made. The implications of the results are also discussed.

Cranking Calculation in the sdg Interacting Boson Model

A self-consistent cranking calculation of the intrinsic states of the sdg interacting boson model is performed. The formulae of the moment of inertia are given in a general sdg IBM multipole Hamiltonian with one- and two-body terms. In the quadrupole interaction, the intrinsic states, the quadrupole and hexadecapole deformation and the moment of inertia are investigated in the large N limit. Using a simple Hamiltonian, the results of numerical calculations for and satisfactorily reproduce the experimental data.

Table of Wigner coefficients

In this paper, algebraic expressions for (lambda, 0) x (4, 0) reduction Wigner coefficients in the SU3 superset of R-3 physical basis are presented. They are obtained by a building-up process. These tables are useful in studies of nuclear algebraic models, such as the sdg interacting boson model.

Spin dependence of intra–ground-state-bandE2transitions in the SU(3) limit of thesdginteracting boson model

B(E2, L+2-->L) transitions in the sdg interacting boson model SU(3) limit are studied with a general E2 transition operator. Analytical expressions are obtained using a group theoretic method. It is found that when using transition operators of the form (d dagger (g) over tilde+g dagger (d) over tilde)(2) or (g dagger (d) over tilde)(2), the B(E2, L+2-->L) values in the groundstate band have an L(L+3) dependent term. As L increases, the B(E2) values can be larger than the rigid rotor model value. Application to U-236,U-238 is discussed. [S0556-2813(98)00804-8].

Description of the Hexadecapole Deformation Parameter in the sdg Interacting Boson Model

The hexadecapole deformation parameter β4 of the rare-earth and actinide nuclei is investigated in the framework of the sdg interacing boson model. An explicit relation between the geometric hexadecapole deformation parameter β4 and the intrinsic deformation parameters ϵ4, ϵ2 are obtained. The deformation parameters β4 of the rare-earths and actinides are determined without any free parameter. The calculated results agree with experimental data well. It also shows that the SU(5) limit of the sdg interacting boson model can describe the β4 systematics as well as the SU(3) limit.

ΔI = 4 Bifurcation and the sdg Interacting Boson Model11The project supported by National Natural Science Foundation of China

We show that the superdeformed nuclear states can be described in the framework of the interacting boson model (IBM) with the g-bosons being taken into account in this paper. The ΔI = 4 bifurcation in superdeformed rotational bands can be reproduced in the SU(5) limit of the sdg IBM. The perturbation causing the ΔI = 4 bifurcation to emerge in the ΔI = 2 superdeformed rotational band may possess the SU(5) symmetry.

Description of deformed nuclei in the sdg boson model

We present a study of deformed nuclei in the framework of the sdg interacting boson model utilizing both numerical diagonalization and analytical $1/N$ expansion techniques. The focus is on description of high-spin states which have recently become computationally accessible through the use of computer algebra in the $1/N$ expansion formalism. A systematic study is made of high-spin states in rare-earth and actinide nuclei.

B(IS4; 0 GS + ?4 ? + ) systematics in rare-earth nuclei: SUsdg (3) description

The observed variation of B(IS4; 0 GS + → + ) with mass number A, that gives information about hexadecupole component inγ-vibration, in rare-earth nuclei is studied in the SUsdg (3) limit of sdg interacting boson model employing IBM-2 to IBM-1 projected hexadecupole transition operator with effective charges determined using a multi-j shell mapping procedure. The SUsdg (3) limit provides a reasonably good description of the data.

Simple model for deriving sdg interacting boson model Hamiltonians: 150Nd example.

A simple and yet useful model for deriving sdg interacting boson model (IBM) Hamiltonians is to assume that single-boson energies derive from identical particle (pp and nn) interactions and proton, neutron single-particle energies, and that the two-body matrix elements for bosons derive from pn interaction, with an IBM-2 to IBM-1 projection of the resulting p-n sdg IBM Hamiltonian. The applicability of this model in generating sdg IBM Hamiltonians is demonstrated, using a single-j-shell Otsuka-Arima-Iachello mapping of the quadrupole and hexadecupole operators in proton and neutron spaces separately and constructing a quadrupole-quadrupole plus hexadecupole-hexadecupole Hamiltonian in the analysis of the spectra, B(E2)'s, and E4 strength distribution in the example of $^{150}\mathrm{Nd}$.

EIKONAL SCATTERING IN THE sdg INTERACTING BOSON MODEL: ANALYTICAL RESULTS IN THE SUsdg(3) LIMIT AND THEIR GENERALIZATIONS

General expression for the representation matrix elements in the SU sdg(3) limit of the sdg interacting boson model (sdgIBM) is derived that determine the scattering amplitude in the eikonal approximation for medium energy proton-nucleus scattering when the target nucleus is deformed and it is described by the SU sdg(3) limit. The SU sdg(3) result is generalized to two important situations: (i) when the target nucleus ground band states are described as states arising out of angular momentum projection from a general single Kπ = 0+ intrinsic state in sdg space; (ii) for rotational bands built on one-phonon excitations in sdgIBM.

Sdg Interacting boson model: hexadecupole degree of freedom in nuclear structure

Thesdg interacting boson model (sdgIBM), which includes monopole (s), quadrupole (d) and hexadecupole (g) degrees of freedom, enables one to analyze hexadecupole (E4) properties of atomic nuclei. Various aspects of the model, both analytical and numerical, are reviewed emphasizing the symmetry structures involved. A large number of examples are given to provide understanding and tests, and to demonstrate the predictiveness of thesdg model. Extensions of the model to include proton-neutron degrees of freedom and fermion degrees of freedom (appropriate for odd mass nuclei) are briefly described. A comprehensive account ofsdgIBM analysis of all the existing data on hexadecupole observables (mainly in the rare-earth region) is presented, includingβ 4 (hexadecupole deformation) systematics,B(IS4; 0 GS + →4 + ) systematics that give information about hexadecupole component in γ-vibration,E4 matrix elements involving few low-lying 4+ levels,E4 strength distributions and hexadecupole vibrational bands in deformed nuclei.

Beta 4 systematics in rare-earth and actinide nuclei: sdg interacting boson model description.

The observed variation of hexadecupole deformation parameter ${\mathrm{\ensuremath{\beta}}}_{4}$ with mass number A in rare-earth and actinide nuclei is studied in the sdg interacting boson model (IBM) using single j-shell Otsuka-Arima-Iachello mapped and IBM-2 to IBM-1 projected hexadecupole transition operator together with ${\mathrm{SU}}_{\mathit{s}\mathit{d}\mathit{g}}$(3) and ${\mathrm{SU}}_{\mathit{s}\mathit{d}\mathit{g}}$(5) coherent states. The ${\mathrm{SU}}_{\mathit{s}\mathit{d}\mathit{g}}$(3) limit is found to provide a good description of data.

Dynamic shape transitions in the sdg boson model

The dynamic evolution of shapes in the sdg interacting boson model is investigated using the angular momentum projected mean field theory. Deformed nuclei are found to be quite stable against shape changes but transitional nuclei could exhibit dynamic shape transitions in the region L = 10-20. Conditions of existence and experimental signatures for dynamic shape transitions are discussed together with a likely candidate, 192Os.

Sdg Interacting boson hamiltonian in the seniority scheme

The sdg interacting boson hamiltonian is derived in the seniority scheme. We use the method of Otsuka, Arima and Iachello in order to derive the boson hamiltonian from the fermion hamiltonian. To examine how good is the boson approximation in the zeroth-order, we carry out the exact shell model calculations in a single j-shell. It is found that almost all low-lying levels are reproduced quite well by diagonalizing the sdg interacting boson hamiltonian in the vibrational case. In the deformed case the introduction of g-bosons improves the reproduction of the spectra and of the binding energies which are obtained by diagonalizing the exact shell model hamiltonian. In particular the sdg interacting boson model reproduces well-developed rotational bands.

Proton-neutron sdg boson model and spherical-deformed phase transition

The spherical-deformed phase transition in nuclei is described in terms of the proton-neutron sdg interacting boson model. The sdg hamiltonian is introduced to model the pairing+quadrupole interaction. The phase transition is reproduced in this framework as a function of the boson number in the Sm isotopes, while all parameters in the hamiltonian are kept constant at values reasonable from the shell-model point of view. The sd IBM is derived from this model through the renormalization of g-boson effects.

E4 properties in deformed nuclei and the sdg interacting boson model.

The hexadecapole transition strength distribution is measured for the deformed nucleus 150Nd using the (p,p') reaction at Ep=30 MeV. The experimental information on B(E4) values in this nucleus and in 156Gd is interpreted in the framework of the sdg interacting boson model. It is found that the main features of the experimental data are fairly well reproduced by a Hartree-Bose method plus Tamm-Dancoff approximation.