Surface Oscillations in Even-Even Nuclei

Wilets, L.; Jean, M.

doi:10.1103/physrev.102.788

Cited by 728 publications

(451 citation statements)

References 7 publications

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“…The γ parameter ranges from 0 • (prolate shape) to 60 • (oblate shape), and maximum triaxiality occurs at 30 • . 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.…”

mentioning

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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mentioning

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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“…Thus, it has rich algebraic, geometrical, and analytical structures all which are exploited in this paper. It has a spectrum generating algebra given by the semi-direct sum Lie algebra [HW (5) [19], and the axially-symmetric rigid-rotor model. These submodels are associated with dynamical subgroup chains corresponding to different paths through the set of groups…”

Section: The Standard Solvable Limits Of the Collective Modelmentioning

confidence: 99%

A computationally tractable version of the collective model

2004

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A computationally tractable version of the Bohr-Mottelson collective model is presented which makes it possible to diagonalize realistic collective models and obtain convergent results in relatively small appropriately chosen subspaces of the collective model Hilbert space. Special features of the proposed model is that it makes use of the beta wave functions given analytically by the softened-beta version of the Wilets-Jean model, proposed by Elliott et al., and a simple algorithm for computing SO(5) ⊃ SO(3) spherical harmonics. The latter has much in common with the methods of Chacon, Moshinsky, and Sharp but is conceptually and computationally simpler. Results are presented for collective models ranging from the sherical vibrator to the Wilets-Jean and axially symmetric rotor-vibrator models.

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“…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 predictions of models involving large rigid triaxiality are very close to the predictions of γ-soft models involving γ-fluctuations such that γ rigid of the former equals γ rms of the latter.…”

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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Surface Oscillations in Even-Even Nuclei

Cited by 728 publications

References 7 publications

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

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

A computationally tractable version of the collective model

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

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