Empirical Realization of a Critical Point Description in Atomic Nuclei

Casten, R. F.; Zamfir, N. V.

doi:10.1103/physrevlett.87.052503

Cited by 385 publications

(313 citation statements)

References 9 publications

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“…Critical point symmetries in nuclear structure are recently receiving considerable attention [1,2,3], since they provide parameter-free (up to overall scale factors) predictions supported by experimental evidence [4,5,6,7]. So far the E(5) [U(5) (vibrational) to O(6) (γ-unstable)] [1,4,5] and the X(5) [U(5) to SU(3) (prolate deformed)] [2,6,7] critical point symmetries have been considered, with the recent addition of Y(5) [3], related to the transition from axial to triaxial shapes.…”

Section: Introductionmentioning

confidence: 99%

“…So far the E(5) [U(5) (vibrational) to O(6) (γ-unstable)] [1,4,5] and the X(5) [U(5) to SU(3) (prolate deformed)] [2,6,7] critical point symmetries have been considered, with the recent addition of Y(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.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Introductionmentioning

confidence: 99%

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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“…Critical point symmetries [1,2] are attracting recently considerable interest, since they provide parameter-independent (up to overall scale factors) predictions supported by experiment [3,4,5,6]. The E(5) [1] and X(5) [2] critical point symmetries have been obtained from the Bohr Hamiltonian [7] after separating variables in different ways and using an infinite square well potential in the β (quadrupole) variable, the latter corresponding to the critical point of the transition from quadrupole vibrations [U (5)] to axial quadrupole deformation [SU(3)] [2].…”

Section: Introductionmentioning

confidence: 99%

“…The E(5) [1] and X(5) [2] critical point symmetries have been obtained from the Bohr Hamiltonian [7] after separating variables in different ways and using an infinite square well potential in the β (quadrupole) variable, the latter corresponding to the critical point of the transition from quadrupole vibrations [U (5)] to axial quadrupole deformation [SU(3)] [2]. A systematic study of phase transitions in nuclear collective models has been given in [8,9,10].…”

Section: Introductionmentioning

confidence: 99%

Parameter-free solution of the Bohr Hamiltonian for actinides critical in the octupole mode

Lenis

Bonatsos

2006

Physics Letters B

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An analytic, parameter-free (up to overall scale factors) solution of the Bohr Hamiltonian involving axially symmetric quadrupole and octupole deformations, as well as an infinite well potential, is obtained, after separating variables in a way reminiscent of the Variable Moment of Inertia (VMI) concept. Normalized spectra and B(EL) ratios are found to agree with experimental data for 226 Ra and 226 Th, the nuclei known to lie closest to the border between octupole deformation and octupole vibrations in the light actinide region. IntroductionCritical point symmetries [1,2] are attracting recently considerable interest, since they provide parameter-independent (up to overall scale factors) predictions supported by experiment [3,4,5,6]. The E(5) [1] and X(5) [2] critical point symmetries have been obtained from the Bohr Hamiltonian [7] after separating variables in different ways and using an infinite square well potential in the β (quadrupole) variable, the latter corresponding to the critical point of the transition from quadrupole vibrations [U(5)] to axial quadrupole deformation [SU(3)] [2]. A systematic study of phase transitions in nuclear collective models has been given in [8,9,10].In the present work a solution of the Bohr Hamiltonian aiming at the description of the transition from axial octupole deformation to octupole vibrations in the light actinides [11] is worked out. In the spirit of E(5) and X(5) the solution involves an infinite square well potential in the deformation variable and leads to parameter-free (up to overal scale factors) predictions for spectra and B(EL) transition rates. Both (axially symmetric) quadrupole and octupole deformations are taken into account, in order to describe low-lying negative parity states related to octupole deformation, known to occur in the light actinides [11]. Separation of variables is achieved in a novel way, reminiscent of the Variable Moment of Inertia (VMI) concept [12]. The parameter-free predictions of the model turn out to be

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“…Understanding the evolution of the nuclear shape and structure as a function of nucleon number between these benchmarks of nuclear quadrupole collectivity is one of the most intriguing tasks of nuclear structure research. To an even larger extent this applies for the regions around the shape transitional points [3,[5][6][7] that are characterized by large fluctuations of the quadrupole shape of the ground state.…”

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confidence: 99%

Absoluteβ-to-ground band transition strengths in154Sm

et al. 2012

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Empirical Realization of a Critical Point Description in Atomic Nuclei

Abstract: It is shown that (152)Sm and other N = 90 isotones are the first empirical manifestation of the newly predicted analytic description of nuclei at the critical point of a vibrator to axial rotor phase transition.

Cited by 385 publications

References 9 publications

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

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

Parameter-free solution of the Bohr Hamiltonian for actinides critical in the octupole mode

Absoluteβ-to-ground band transition strengths in154Sm

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