Description of nuclear octupole and quadrupole deformation close to axial symmetry: Critical-point behavior of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mmultiscripts><mml:mi mathvariant="normal">Ra</mml:mi><mml:mprescripts /><mml:none /><mml:mrow><mml:mn>224</mml:mn></mml:mrow></mml:mmultiscripts></mml:math>and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mmultiscripts><mml:mi mathvariant="normal">Th</mml:mi><mml:mprescripts /><mml:none

Bizzeti, P. G.; Bizzeti‐Sona, A. M.

doi:10.1103/physrevc.77.024320

Cited by 40 publications

(34 citation statements)

References 29 publications

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“…(21) the integration over the Euler angles θ involves standard integrals over three Wigner functions calculated in Appendix B, while the rest of the integrations are performed over β 3 2 dβ 2 β 3 3 dβ 3 , where the β 3 2 , β 3 3 factors come from the volume element and cancel with the first factor of Eq. (20). Using Eqs.…”

Section: B Theβ Part Of the Spectrummentioning

confidence: 99%

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Octupole deformation in light actinides within an analytic quadrupole octupole axially symmetric model with a Davidson potential

Bonatsos

Martinou²,

Minkov³

et al. 2015

Phys. Rev. C

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The analytic quadrupole octupole axially symmetric model, which had successfully predicted 226 Ra and 226 Th as lying at the border between the regions of octupole deformation and octupole vibrations in the light actinides using an infinite well potential (AQOA-IW), is made applicable to a wider region of nuclei exhibiting octupole deformation, through the use of a Davidson potential, β 2 + β 4 0 /β 2 (AQOA-D). Analytic expressions for energy spectra and B(E1), B(E2), B(E3) transition rates are derived. The spectra of 222−226 Ra and 224,226 Th are described in terms of the two parameters φ0 (expressing the relative amount of octupole vs. quadrupole deformation) and β0 (the position of the minimum of the Davidson potential), while the recently determined B(EL) transition rates of 224 Ra, presenting stable octupole deformation, are successfully reproduced. A procedure for gradually determining the parameters appearing in the B(EL) transitions from a minimum set of data, thus increasing the predictive power of the model, is outlined.

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Section: B Theβ Part Of the Spectrummentioning

confidence: 99%

“…2) In the AQOA model the symmetry axes of the quadrupole and octupole deformations are taken to coincide, in order to guarantee axial symmetry, while in the more general framework of Refs. [19,20] nonaxial contributions, small but not frozen to zero, are taken into account.…”

Section: Introductionmentioning

confidence: 99%

Octupole deformation in light actinides within an analytic quadrupole octupole axially symmetric model with a Davidson potential

Bonatsos

Martinou²,

Minkov³

et al. 2015

Phys. Rev. C

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“…The formulation of X(5) attracted immediate attention both experimentally and theoretically. Soon after the introduction of the X (5) [35,36], although the last two candidates could be better described by combining quadrupole and octupole degrees of freedom [37][38][39]. Concerning theoretical extensions of X(5), Bonatsos and collaborators studied a sequence of potentials of the type β 2n , which allows one to go from the vibrational limit, n = 1, to X(5), n → ∞ [40].…”

Section: Introductionmentioning

confidence: 99%

Relationship between X(5) models and the interacting boson model

García‐Ramos

Arias

2010

Phys. Rev. C

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The connections between the X(5) models [the original X(5) using an infinite square well, X(5)-β 8 , X(5)-β 6 , X(5)-β 4 , and X(5)-β 2 ], based on particular solutions of the geometrical Bohr Hamiltonian with harmonic potential in the γ degree of freedom, and the interacting boson model (IBM) are explored. This work is the natural extension of the work presented in García-Ramos and Arias, Phys. Rev. C 77, 054307 (2008) for the E(5) models. For that purpose, a quite general one-and two-body IBM Hamiltonian is used and a numerical fit to the different X(5) model energies is performed; then the obtained wave functions are used to calculate B(E2) transition rates. It is shown that within the IBM one can reproduce well the results for energies and B(E2) transition rates obtained with all these X(5) models, although the agreement is not so impressive as for the E(5) models. From the fitted IBM parameters the corresponding energy surface can be extracted and, surprisingly, only the X(5) case corresponds in the moderately large N limit to an energy surface very close to the one expected for a critical point, whereas the rest of models are situated a little further away.

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“…In Refs. [20,21], the Bohr Hamiltonian with the collective coordinates involving quadrupole and octupole deformations has been introduced to describe the SE/SPT for Ra and Th isotopes, and 224 Ra and 224 Th are suggested to be the point of SPT from spherical to octupole-deformed shapes.Recently, an axial-symmetric reflection asymmetric relativistic mean-field (RAS-RMF) theory [22] has been developed. Its application to the shape evolution for Sm isotopes is presented in Ref. [23], where the shape/phase transition from U(5) to SU(3) symmetry is marked clearly with the possible octupole degree of freedom included.…”

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confidence: 99%

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confidence: 99%

Microscopic description of nuclear shape evolution from spherical to octupole-deformed shapes in relativistic mean-field theory

2010

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Reflection asymmetric relativistic mean-field theory is used to investigate the shape evolution for even-even Th isotopes. The calculated deformations, matter density distributions, and potential energy surfaces demonstrate clearly the shape evolution from spherical to octupole deformed. Especially, it is shown that Th isotopes suffer two types of shape transition when the neutron number increases from N = 126 to N = 156. One is from spherical to octupole deformed around N = 134, and another is from octupole to quadrupole deformed around N = 150.The equilibrium shape of atomic nuclei as well as the transition between the different shapes has been the subject of a large number of theoretical and experimental studies (for a review, see, for example, Ref.[1] and references therein). Theoretical studies have typically been based on phenomenological geometric models of nuclear shapes and potentials [2], or algebraic models of nuclear structure [3], which have gained remarkable success in describing the phenomena of shape evolution and shape phase transition (SE/SPT) [4][5][6]. However, to provide greater detail, it is necessary to perform microscopic investigation of SE/SPT. In Ref.[7], the microscopic relativistic mean-field (RMF) theory is applied to Sm isotopes and the SE/SPT from spherical to axially deformed shapes is demonstrated clearly. In Ref.[8], a series of isotopes suggested as exhibiting critical-point symmetries are investigated by the microscopic approach. In combination with generator coordinate method (GCM), RMF theory has presented an excellent description of the general features of the transitions between spherical and axially deformed nuclei, the singular properties of excitation spectra, and the transition rates at the critical point of SPT [9]. In Ref.[10], the triaxial RMF theory is developed. In combination with GCM, the triaxial RMF theory has provided the deformation parameters to solve the five-dimensional collective Hamiltonian, which has presented a good description of the quantum phase transition between spherical and axially deformed shapes, as well as between spherical and triaxially deformed shapes [11][12][13]. Similar checks are performed for nuclear SE/SPT by using nonrelativistic microscopic approaches, including the self-consistent Skyrme-Hartree-Fock + BCS approximation, the Hartree-Fock-Bogoliubov approximation based on Gogny interaction, etc. The details can be found in the recent literature [14][15][16][17].All these studies only relate to the phase transition between spherical and quadrupole shapes. However, in the Ra-Th region, it was observed that the nuclei 224 Ra and 224 Th, which have a very low-lying negative-parity band, soon merge with the positive-parity one for J > 5, which * jianyou@ahu.edu.cn implies that the octupole deformation should not be ignored in discussing the behavior of the phase transition [18,19]. In Refs. [20,21], the Bohr Hamiltonian with the collective coordinates involving quadrupole and octupole deformations has been introduced to describe the SE...

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Description of nuclear octupole and quadrupole deformation close to axial symmetry: Critical-point behavior ofRa224andTh

Cited by 40 publications

References 29 publications

Octupole deformation in light actinides within an analytic quadrupole octupole axially symmetric model with a Davidson potential

Octupole deformation in light actinides within an analytic quadrupole octupole axially symmetric model with a Davidson potential

Relationship between X(5) models and the interacting boson model

Microscopic description of nuclear shape evolution from spherical to octupole-deformed shapes in relativistic mean-field theory

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