X(3): an exactly separable γ-rigid version of the X(5) critical point symmetry

Bonatsos, Dennis; Lenis, D.; Petrellis, D.; Terziev, P. A.; Yigitoglu, I.

doi:10.1016/j.physletb.2005.10.060

Cited by 118 publications

(139 citation statements)

References 25 publications

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“…J is the spin of the level, τ = J/2, and n w is the wobbling quantum number [8] which is zero for 0 + states. X(3) [27] [similar to X(5), but with γ fixed to 0], they increase as n(n + 2), as also shown in Table 2. These results can be easily interpreted [3] by taking into account the order of the Bessel functions appearing as eigenfunctions in these models, given in Table 3, as well as the fact that the spectra of the Bessel functions J ν are found to increase approximately as n(n + ν + 3/2), this result being exact only for ν = 1/2 [3].…”

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confidence: 59%

0[sup +] states in the large boson number limit of the Interacting Boson Approximation model

Bonatsos¹,

McCutchan²,

Casten³

2008

AIP Conference Proceedings

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Abstract.Studies of the Interacting Boson Approximation (IBA) model for large boson numbers have been triggered by the discovery of shape/phase transitions between different limiting symmetries of the model. These transitions become sharper in the large boson number limit, revealing previously unnoticed regularities, which also survive to a large extent for finite boson numbers, corresponding to valence nucleon pairs in collective nuclei. It is shown that energies of 0 + n states grow linearly with their ordinal number n in all three limiting symmetries of IBA [U(5), SU(3), and O(6)]. Furthermore, it is proved that the narrow transition region separating the symmetry triangle of the IBA into a spherical and a deformed region is described quite well by the degeneracies E(0, while the energy ratio E(6 + 1 )/E(0 + 2 ) turns out to be a simple, empirical, easy-to-measure effective order parameter, distinguishing between first-and second-order transitions. The energies of 0 + n states near the point of the first order shape/phase transition between U(5) and SU(3) are shown to grow as n(n+3), in agreement with the rule dictated by the relevant critical point symmetries resulting in the framework of special solutions of the Bohr Hamiltonian. The underlying partial dynamical symmetries and quasi-dynamical symmetries are also discussed. The Interacting Boson Approximation (IBA) model [1], describing collective phenomena in atomic nuclei in terms of s and d bosons (of angular momentum 0 and 2, respectively), is known to possess an overall U(6) symmetry, containing three different dynamical symmetries, U(5), SU(3), and O(6), corresponding to near-spherical (vibrational), axially symmetric prolate deformed (rotational), and soft with respect to axial asymmetry (γ-unstable) nuclei respectively. These limiting symmetries are shown at the vertices of the symmetry triangle [2] of the model, shown in Fig. 1. KeywordsAn energy functional can be obtained [4] in the classical limit of the model, through the use of the coherent state formalism [5,6]. Studying this energy functional in the framework of catastrophe theory one can see [7] that a first order phase transition (in the Ehrenfest classification) is predicted to occur between the limiting symmetries U(5) and SU(3), while a second order phase transition is expected between U(5) and O(6). We refer to these transitions as shape/phase transitions. A narrow shape coexistence region is then predicted [4] in the symmetry triangle of the IBA, separating the spherical and deformed phases. The shape coexistence region shrinks into the point of second order phase transition as the U(5)-O(6) line is approached, as shown in Fig. 1.

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confidence: 59%

0[sup +] states in the large boson number limit of the Interacting Boson Approximation model

Bonatsos¹,

McCutchan²,

Casten³

2008

AIP Conference Proceedings

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“…In particular, the critical point of the spherical to γ-unstable shape transition [1], called E (5), and the critical point from the spherical to axially deformed shape [2], called X(5), have been confirmed by experiment [23][24][25][26]. In view of their successful application in helping to understand even-even systems, it seems critical point symmetries in odd-A systems warrant further investigation.…”

Section: Introductionmentioning

confidence: 99%

“…Recently, critical point symmetries [1][2][3][4][5] have attracted considerable attention, since they provide benchmark results for the study of even-even nuclei as they undergo a transition between two different phases (shapes) [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22]. In particular, the critical point of the spherical to γ-unstable shape transition [1], called E (5), and the critical point from the spherical to axially deformed shape [2], called X(5), have been confirmed by experiment [23][24][25][26].…”

Section: Introductionmentioning

confidence: 99%

“…In this article, we propose an exactly solvable model, called X(3/ 2j+1), based on the X(3) critical point symmetry [5]. Although the original X(5/ 2j+1) model was designed to describe the similar physical situation, it can only be solved analytically within an approximation as shown in [30], where the coupling strength between the even-even core and single-j particle is taken as the same value for different odd-A nuclei.…”

Section: Introductionmentioning

confidence: 99%

“…As the X(5) symmetry seems well confirmed in experiment [2], it provides a better test for exploring effects of the X(5) critical point symmetry in odd-A nuclei near the even-even partners at the X(5) critical point. Very recently, in the same spirit as the E(5/4) and E(5/12) examples, an X(5/ 2j+1) model that coupled a spin-j particle to the X(5) symmetry core was advanced [30].In this article, we propose an exactly solvable model, called X(3/ 2j+1), based on the X(3) critical point symmetry [5]. Although the original X(5/ 2j+1) model was designed to describe the similar physical situation, it can only be solved analytically within an approximation as shown in [30], where the coupling strength between the even-even core and single-j particle is taken as the same value for different odd-A nuclei.…”

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confidence: 98%

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Simple description of odd-Anuclei around the critical point of the spherical to axially deformed shape phase transition

et al. 2011

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An analytically solvable model, X(3/ 2j + 1), is proposed to describe odd-A nuclei near the X(3) critical point. The model is constructed based on a collective core described by the X(3) critical point symmetry coupled to a spin-j particle. A detailed analysis of the spectral patterns for j = 1/2, 3/2 cases is provided to illustrate dynamical features of the model. Through comparing the theory with experimental data and results of other models, it is found that the X(3/ 2j + 1) model can be taken as a simple yet very effective scheme to describe those odd-A nuclei with an even-even core at the critical point of the spherical to axially deformed shape phase transition. I. IntroductionRecently, critical point symmetries [1][2][3][4][5] have attracted considerable attention, since they provide benchmark results for the study of even-even nuclei as they undergo a transition between two different phases (shapes) [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22]. In particular, the critical point of the spherical to γ-unstable shape transition [1], called E(5), and the critical point from the spherical to axially deformed shape [2], called X(5), have been confirmed by experiment [23][24][25][26]. In view of their successful application in helping to understand even-even systems, it seems critical point symmetries in odd-A systems warrant further investigation. And since the low-lying structures of two adjacent nuclei with more or less than one neutron or proton should be driven by similar collective considerations, the critical point symmetries observed in even-even systems should also be evident in the adjacent odd-A nuclei. The first case of a critical point Bose-Fermi symmetry, called E(5/4) [27], was developed by Iachello to describe, analytically, the γ-soft critical point E(5) configuration coupled to a j = 3/2 particle.135 Ba was suggested as an empirical example of E(5/4) symmetry, with a report of a detailed analysis given in [28]. While these results show significant agreement between theory and experiment, there are also some differences. Another critical point Bose-Fermi symmetry, called E(5/12) [29], was developed by Alonso, Arias, and Vitturi, who extended the case of the E(5/4) symmetry with a spin-j particle into the multi-j case with j = 1/2, 3/2, 5/2. Both the E(5/4) and E(5/12) models were developed to describe odd-A nuclei near even-even nuclei that display the E(5) critical point symmetry [1]; that is, nuclei in the spherical to γ-unstable transitional region. As the X(5) symmetry seems well confirmed in experiment [2], it provides a better test for exploring effects of the X(5) critical point symmetry in odd-A nuclei near the even-even partners at the X(5) critical point. Very recently, in the same spirit as the E(5/4) and E(5/12) examples, an X(5/ 2j+1) model that coupled a spin-j particle to the X(5) symmetry core was advanced [30].In this article, we propose an exactly solvable model, called X(3/ 2j+1), based on the X(3) critical point symmetry [5]. Although the original X(5/ ...

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Critical point symmetry for odd-odd nuclei and collective multiple chiral doublet bands

Zhang

2021

Sci. China Phys. Mech. Astron.

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A critical point symmetry (CPS) for odd-odd nuclei is built in the core-particle coupling scheme with the even-even core assumed to follow the spherical to triaxially deformed shape phase transition. It is shown that the model Hamiltonian can be approximately solved with the solutions being expressed in terms of the Bessel functions of irrational orders. In particular, the CPS predicts that collective multiple chiral doublets may exist in transitional odd-odd systems.collective model, critical point symmetry, multiple chiral doublet bands

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X(3): an exactly separable γ-rigid version of the X(5) critical point symmetry

Cited by 118 publications

References 25 publications

0[sup +] states in the large boson number limit of the Interacting Boson Approximation model

0[sup +] states in the large boson number limit of the Interacting Boson Approximation model

Simple description of odd-Anuclei around the critical point of the spherical to axially deformed shape phase transition

Critical point symmetry for odd-odd nuclei and collective multiple chiral doublet bands

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