The Interacting Boson Model

Iachello, F.; Arima, A.

doi:10.1017/cbo9780511895517

Cited by 2,004 publications

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“…The truncation of the model space, however, by concentrating on nucleon pair modes (mainly 0 + and 2 + coupled pairs, to be treated as bosons within the Interacting Boson Approximation (IBM) [28]), has made the calculations feasible, even including pair excitations across the Z = 82 shell closure [29] in the Pb region. More in particular, the Pb nuclei have been extensively studied giving rise to bands with varying collectivity depending on the nature of the excitations treated in the model space [11,30,31,32,33,34,35,36,37].…”

Section: Introductionmentioning

confidence: 99%

The Pt isotopes: Comparing the Interacting Boson Model with configuration mixing and the extended consistent-Q formalism

García-Ramos

Heyde²

2009

Nuclear Physics A

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The role of intruder configurations in the description of energy spectra and B(E2) values in the Pt region is analyzed. In particular, we study the differences between Interacting Boson Model calculations with or without the inclusion of intruder states in the even Pt nuclei 172−194 Pt. As a result, it shows that for the description of a subset of the existing experimental data, i.e., energy spectra and absolute B(E2) values up to an excitation energy of about 1.5 MeV, both approaches seem to be equally valid. We explain these similarities between both model spaces through an appropriate mapping. We point out the need for a more extensive comparison, encompassing a data set as broad (and complete) as possible to confront with both theoretical approaches in order to test the detailed structure of the nuclear wave functions. 21.60.Fw. PACS

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Section: Introductionmentioning

confidence: 99%

The Pt isotopes: Comparing the Interacting Boson Model with configuration mixing and the extended consistent-Q formalism

García-Ramos

Heyde²

2009

Nuclear Physics A

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“…No critical point symmetry for the prolate to oblate shape phase transition originating from the Bohr equation has been given so far, although it has been suggested [10,11] that the (parameter-dependent) O(6) limit of the Interacting Boson Model (IBM) [12] can serve as the critical point of this transition, since various physical quantities exhibit a drastic change of behaviour at O(6), as they should [13].…”

Section: Introductionmentioning

confidence: 99%

Z(5): critical point symmetry for the prolate to oblate nuclear shape phase transition

et al. 2004

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A critical point symmetry for the prolate to oblate shape phase transition is introduced, starting from the Bohr Hamiltonian and approximately separating variables for γ = 30 o . Parameter-free (up to overall scale factors) predictions for spectra and B(E2) transition rates are found to be in good agreement with experimental data for 194 Pt, which is supposed to be located very close to the prolate to oblate critical point, as well as for its neighbours ( 192 Pt, 196 (5) [3], related to the transition from axial to triaxial shapes. All these critical point symmetries have been constructed by considering the original Bohr equation [8], separating the collective β and γ variables, and making different assumpions about the u(β) and u(γ) potentials involved.Furthermore, it has been demonstrated [9] that experimental data in the Hf-Hg mass region indicate the presence of a prolate to oblate shape phase transition, the nucleus 194 Pt being the closest one to the critical point. No critical point symmetry for the prolate to oblate shape phase transition originating from the Bohr equation has been given so far, although it has been suggested [10,11] that the (parameter-dependent) O(6) limit of the Interacting Boson Model (IBM) [12] can serve as the critical point of this transition, since various physical quantities exhibit a drastic change of behaviour at O(6), as they should [13].In the present work a parameter-free (up to overall scale factors) critical point symmetry, to be called Z(5), is introduced for the prolate to oblate shape phase transition, leading to parameter-free predictions which compare very well with the experimental data for 194 Pt. The path followed for constructing the Z(5) critical point symmetry is described here: 1) Separation of variables in the Bohr equation [8] is achieved by assuming γ = 30 o . When considering the transition from γ = 0 o (prolate) to γ = 60 o (oblate), it is reasonable to expect that the triaxial region (0 o < γ < 60 o ) will be crossed, γ = 30 o lying in its middle. Indeed, there is experimental evidence supporting this assumption [14].2) For γ = 30 o the K quantum number (angular momentum projection on the bodyfixedẑ ′ -axis) is not a good quantum number any more, but α, the angular momentum projection on the body-fixedx ′ -axis is, as found [15] in the study of the triaxial rotator [16,17].3) Assuming an infinite well potential in the β-variable and a harmonic oscillator potential having a minimum at γ = 30 o in the γ-variable, the Z(5) model is obtained.On these choices, the following comments apply: 1) Taking γ = 30 o does not mean that rigid triaxial shapes are prefered. In fact, it has been pointed out [18] that a nucleus in a γ-flat potential [19] (as it should be expected for a prolate to oblate shape phase transition) oscillates uniformly over γ from γ = 0 o to γ = 60 o , having an average value of γ av = 30 o , and, therefore, the triaxial case to which it should be compared is the one with γ = 30 o . Furthermore, it is known [20] that many prediction...

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“…At the lowest spins, however, especially in the ground state itself, triaxial structures have typically been ascribed to pronounced γ softness, corresponding to a broad minimum in γ . This type of nuclei closely relates to the O(6) dynamical symmetry limit of the IBM-1, with the best known example being 196 Pt [6,[17][18][19].…”

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confidence: 97%

“…The rigid triaxial rotor model by Davydov and Filippov [2] considers a well-defined minimum for a certain value of γ in the potential energy surface while the model by Wilets and Jean [3] treats the potential independently of γ , called γ soft. More microscopic models, such as the shell model [4,5], the algebraic interacting boson model (IBM) [6], mean field approaches (e.g., Ref. [7]), or energy density functional-based models (e.g., Ref.…”

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confidence: 99%

Triaxiality of neutron-rich Ge84,86,88 from low-energy nuclear spectra

Lettmann¹,

Werner²,

Pietralla³

et al. 2017

Phys. Rev. C

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γ -ray transitions between low-spin states of the neutron-rich 84,86,88 Ge were measured by means of in-flight γ -ray spectroscopy at 270 MeV/u. Excited 6 + 1 , 4 + 1,2 , and 2 + 1,2 states of 84,86 Ge and 4 + 1 and 2 + 1,2 states of 88 Ge were observed. Furthermore, a candidate for a 3 + 1 state of 86 Ge was identified. This state plays a key role in the discussion of ground-state triaxiality of 86 Ge, along with other features of its low-energy level scheme. A new region of triaxially deformed nuclei is proposed in the Ge isotopic chain.

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The Interacting Boson Model

Cited by 2,004 publications

References 0 publications

The Pt isotopes: Comparing the Interacting Boson Model with configuration mixing and the extended consistent-Q formalism

The Pt isotopes: Comparing the Interacting Boson Model with configuration mixing and the extended consistent-Q formalism

Z(5): critical point symmetry for the prolate to oblate nuclear shape phase transition

Triaxiality of neutron-rich Ge84,86,88 from low-energy nuclear spectra

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