Phase transitions and critical points in the rare-earth region

Ramos, J. E. García; Arias, J. M.; Barea, J.; Frank, A.

doi:10.1103/physrevc.68.024307

Cited by 50 publications

(45 citation statements)

References 51 publications

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“…In Ref. [20], a systematic study of isotope chains in the rare-earth region including 144 66 Dy isotope chains was presented. The most general (up to two-body terms) IBM Hamiltonian was used, and for each isotope chain a general fit was performed in such a way that all parameters but one were kept fixed to describe the whole chain.…”

Section: U(5) To Su(3) Transition: Rare-earth Isotopesmentioning

confidence: 99%

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Shape-phase transitions and two-particle transfer intensities

Fossión¹,

Alonso

Arias

et al. 2007

Phys. Rev. C

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In the light of renewed interest in experiments on two-particle transfer reactions, we study the evolution of the transfer spectroscopic intensities as a possible signature of shape-phase transitions. The study is carried out considering chains of even-even nuclei displaying changes in shape, such as from sphericity to axial-symmetric deformed or from sphericity to deformed γ -unstable nuclei. The evolution of the structure of these nuclei is described in terms of the interacting boson model. In correspondence to the critical points characterizing the phase transitions, the ground-to-ground two-particle transfer matrix elements display a rapid discontinuity, with a corresponding increase in the transition to the excited 0 + states. Simple formulas are given using the intrinsic-frame formalism.

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Section: U(5) To Su(3) Transition: Rare-earth Isotopesmentioning

confidence: 99%

“…In Ref. [20], the energy surfaces were calculated and the catastrophe theory was used to determine critical points for each isotope chain. For all these chains, the shapes of the light isotopes are close to sphericity, while the shapes of the heavy ones are close to axial deformations.…”

Section: U(5) To Su(3) Transition: Rare-earth Isotopesmentioning

confidence: 99%

Shape-phase transitions and two-particle transfer intensities

Fossión¹,

Alonso

Arias

et al. 2007

Phys. Rev. C

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“…The details of this calculation will be reported in a longer publication [8]. Suffice it to say here that the procedure is closely related to the one followed by García-Ramos et al [9] and yields a root-mean square deviation for an entire isotopic chain which is typically of the order of 100 keV. In deformed nuclei one adjusts the IBM Hamiltonian to the observed ground-state band and β-and γ-vibrational bands, if known.…”

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Correlating Radii and Electric Monopole Transitions of Atomic Nuclei

et al. 2008

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A systematic analysis of the spherical-to-deformed shape phase transition in even-even rare-earth nuclei from 58Ce to 74W is carried out in the framework of the interacting boson model. These results are then used to calculate nuclear radii and electric monopole (E0) transitions with the same effective operator. The influence of the hexadecapole degree of freedom (g boson) on the correlation between radii and E0 transitions thus established, is discussed.PACS numbers: 21.10. Ft, 21.10.Ky, 21.60.Ev, 21.60.Fw Electric monopole (E0) transitions between nuclear levels proceed mainly by internal conversion with no transfer of angular momentum to the ejected electron. For transition energies greater than 2m e c 2 , electronpositron pair creation is also possible; two-photon emission is possible at all energies but extremely improbable. The total probability for a transition between initial and final states |i and |f can be separated into an electronic and a nuclear factor, P = Ωρ 2 , where the nuclear factorwith R = r 0 A 1/3 (r 0 = 1.2 fm) and where the summation runs over the Z protons in the nucleus. The coefficient σ depends on the assumed nuclear charge distribution but in any reasonable case it is smaller than 0.1 and can be neglected if the leading term is not too small [1]. The charge radius of a state |s is given byIt is found experimentally that the addition of neutrons produces a change in the nuclear charge distribution, an effect which can be parametrized by means of neutron and proton effective charges e n and e p in the charge radius operatorT (r 2 ). This leads to the following generalization of Eq. (2):where the sum is over all nucleons and e k = e n (e p ) if k is a neutron (proton). An obvious connection between ρ and the nuclear charge radius is established in the approximation σ = 0 (which henceforth will be made). Again because of the polarization effect of the neutrons, one introduces an E0 operator of the form [2]The ρ defined in Eq.(1) with σ = 0 is then given by ρ = f|T (E0)|i /eR 2 . The basic hypothesis of this Letter is to assume that the effective nucleon charges in the charge radius and E0 transition operators are the same. If this is so, comparison of Eqs. (3) and (4) leads to the relationAt present, a quantitative test of the correlations between radii and E0 transitions implied by (5) cannot be obtained in the context of the nuclear shell model. The main reason is that E0 transitions between states in a single harmonic-oscillator shell vanish identically [3] and a non-zero E0 matrix element is obtained only if valence nucleons are allowed to occupy at least two oscillator shells. This renders the shell-model calculation computationally challenging (if not impossible), certainly in the heavier nuclei which are considered here. We have therefore chosen to test the implied correlations in the context of a simpler approach, namely the interacting boson model (IBM) of atomic nuclei [4]. In this model low-lying collective excitations of nuclei are described in terms of N b bosons distrib...

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“…[21]). Given the considerable success of these phenomenological studies, one expects that the microscopically-formulated IBM could also have the potential ability to reproduce the QPT.…”

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Shape phase transitions in the interacting boson model: Phenomenological versus microscopic descriptions

et al. 2012

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We investigate the shape phase transition in even-even 64Gd and 66Dy isotopes within the protonneutron interacting boson model (IBM-2). The parameters of the IBM-2 Hamiltonian are fixed by two different ways: the usual phenomenological fitting calculation and the mapping of the constrained self-consistent mean-field calculation with the Skyrme energy density functional onto the appropriate boson system. Notable difference is found between the energy surfaces for the phenomenological and the mapped IBM-2. Key quantities for the collective structural evolution, including level energies, B(E2) values, quadrupole moments and the two-neutron separation energies, are analyzed in comparison to the experimental data. We show that the transition in these quantities occurs rapidly with the neutron number in the IBM-2 phenomenology but that is somewhat smeared out in the mapped IBM-2. The difference in the measurable quantities arises consistently with what is suggested by the energy-surface analysis.

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Phase transitions and critical points in the rare-earth region

Cited by 50 publications

References 51 publications

Shape-phase transitions and two-particle transfer intensities

Shape-phase transitions and two-particle transfer intensities

Correlating Radii and Electric Monopole Transitions of Atomic Nuclei

Shape phase transitions in the interacting boson model: Phenomenological versus microscopic descriptions

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