Description of shape coexistence in 
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 based on the quadrupole-collective Bohr Hamiltonian

Sazonov, D. A.; Kolganova, E. A.; Shneidman, T. M.; Jolos, R. V.; Pietralla, N.; Witt, William Edward

doi:10.1103/physrevc.99.031304

Cited by 24 publications

(14 citation statements)

References 49 publications

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“…It turned out to be not the only doubly-closed shell nucleus to exhibit such shape coexistence structure. The nuclei 40 Ca, 56 Ni, but not only, have more recently indicated the appearance of bands pointing to strongly deformed structures [2][3][4][5]. The same, what was called shape coexistence, was observed in the heavy singleclosed shell nuclei such as the Pb isotopes and the Sn nuclei, with unambiguous indications of experimental evidence for the appearance of deformed bands (see [6] for a review).…”

Section: Introductionmentioning

confidence: 85%

Quest of shape coexistence in Zr isotopes

García‐Ramos

Heyde

2019

Phys. Rev. C

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Background: The mass region with A ≈ 100 and Z ≈ 40 is known to experience a sudden onset of deformation. The presence of the subshell closure Z = 40 makes feasible to create particle-hole excitations at a moderate excitation energy and, therefore, likely intruder states could be present in the low-lying spectrum. In other words, shape coexistence is expected to be a key ingredient to understand this mass region.Purpose: The aim of this work is to describe excitation energies, transition rates, radii, and twoneutron separation energies for the even-even 94−110 Zr nuclei and, moreover, to obtain information about wave functions and deformation.Method: The interacting boson model with configuration mixing will be the framework to study the even-even Zr nuclei, considering only two types of configurations: 0particle-0hole and 2particle-2hole excitations. On one hand, the parameters appearing in the Hamiltonian and in the E2 transition operator are fixed trough a least-squares fit to the whole available experimental information. On the other hand, once the parameters have been fixed, the calculations allow to obtain a complete set of observables for the whole even-even Zr chain of isotopes.Results: Spectra, transition rates, radii, ρ 2 (E0), and two-neutron separation energies have been calculated and a good agreement with the experimental information has been obtained. Moreover, a detailed study of the wave function has been conducted and mean-field energy surfaces and deformation have been computed too.Conclusions: The importance of shape coexistence has been shown to correctly describe the A ≈ 100 mass area for even-even Zr nuclei. This work confirmed the rather spherical nature of the ground state of 94−98 Zr and its deformed nature for 100−110 Zr isotopes. The sudden onset of deformation in 100 Zr is owing to the rapid lowering of a deformed (intruder) configuration which is high-lying in lighter isotopes. 21.60.Fw

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Section: Introductionmentioning

confidence: 85%

Quest of shape coexistence in Zr isotopes

García‐Ramos

Heyde

2019

Phys. Rev. C

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“…In recent years a number of experimental and theoretical studies of the spectroscopy of even-even Zr isotopes have been reported. Most recent experimental results have suggested shape coexistence in 96 Zr [3] and 98 Zr [4,5], a quantum phase transition around the neutron number N ≈ 60 [6,7], and γ-soft and triaxial shapes at 100,102 Zr [8]. Theoretical studies have generally confirmed the interpretation of these experimental findings [3,[9][10][11][12].…”

Section: Introductionmentioning

confidence: 85%

“…Most recent experimental results have suggested shape coexistence in 96 Zr [3] and 98 Zr [4,5], a quantum phase transition around the neutron number N ≈ 60 [6,7], and γ-soft and triaxial shapes at 100,102 Zr [8]. Theoretical studies have generally confirmed the interpretation of these experimental findings [3,[9][10][11][12]. The neighbouring odd-A Zr nuclei have also been extensively studied in experiments.…”

Section: Introductionmentioning

confidence: 91%

Shape phase transitions in odd-A Zr isotopes

Nomura,

Nikšić,

Vretenar

2020

Preprint

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Spectroscopic properties that characterize shape phase transitions in neutron-rich odd-A Zr isotopes are investigated using the framework of nuclear density functional theory and particle-core coupling. The interacting-boson Hamiltonian of the even-even core nuclei, and the single-particle energies and occupation probabilities of the unpaired neutron are completely determined by deformation constrained self-consistent mean-field calculations based on the relativistic Hartree-Bogoliubov model with a choice of a universal energy density functional and pairing interaction. The triaxial (β, γ) deformation energy surfaces for even-even 94−102 Zr indicates transition from triaxial or γ-soft ( 94,96 Zr) to prolate ( 98 Zr), and triaxial ( 100,102 Zr) shapes. The corresponding low-energy excitation spectra of the odd-A Zr isotopes are in very good agreement with recent experimental results. Consistent with the structural evolution of the neighboring even-even Zr nuclei, the statedependent effective deformations and their fluctuations in the odd-A isotopes indicate a pronounced discontinuity around the transitional nucleus 99 Zr.

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“…To describe the shape of V (β) for 96 Zr we have defined in [57] several points fixing the positions of the spherical and deformed minima, the rigidity of the potential near its minima, and the height and width of the barrier separating two minima. Then we vary the positions of the selected points in order to get a satisfactory description of the experimental data.…”

Section: Hamiltonianmentioning

confidence: 99%

“…These investigations were based either on the nuclear Shell Model, or on the Hartree-Fock-Bogoliubov approach and on the Energy Density Functional . The second group includes studies based mainly on the phenomenological models [48][49][50][51][52][53][54][55][56][57][58]. Their aim was to achieve the best possible description of experimental data on Zr isotopes, fixing the model parameters for this purpose.…”

Section: Introductionmentioning

confidence: 99%

Evolution of the phenomenologically determined collective potential along the chain of Zr isotopes

Mardyban,

Kolganova,

Shneidman

et al. 2021

Preprint

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Background: The properties of the collective low-lying states of Zr isotopes which include excitation energies and E2 reduced transition probabilities indicate that some of these states are mainly spherical and the other are mainly deformed ones. A consideration of these data in the framework of the Geometrical Collective Model with β, γ, and rotational degrees of freedom is necessary for 92−102 Zr.Purpose: To investigate the properties of the low-lying collective states of 92−102 Zr based on the five-dimensional Geometrical Quadrupole Collective Model, to obtain the collective potentials for the chains of Zr isotopes and to investigate their evolution with increase of the number of neutrons.Method: The quadrupole-collective Bohr Hamiltonian depending on both β and γ shape variables with a potential having spherical and deformed minima, is applied. The relative depth of two minima, height and width of the barrier, rigidity of the potential near both minima are determined so as to achieve the best possible description of the observed properties of the low-lying collective quadrupole states of 92−102 Zr.Results: Satisfactory agreement with the experimental data on the excitation energies and the E2 reduced transition probabilities is obtained. The evolution of the collective potential with increase of A is described and the distributions of the wave functions of the collective states in β − γ plane are found. Conclusion:It is shown that the low-energy structure of 92−102 Zr can be described in a satisfactory way within the Geometrical Collective Model with the Bohr Hamiltonian. The β-dependence of the potential energy is fixed to describe the experimental data in a best possible way. The resulting potential evolves with A increase from having only one spherical minimum in 92 Zr, through the potentials having both spherical and deformed minima, to the potential with one deformed minimum in 102 Zr. A β-dependence of the wave functions is presented in a set of figures illustrating their distribution over β.

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Description of shape coexistence in Zr96 based on the quadrupole-collective Bohr Hamiltonian

Cited by 24 publications

References 49 publications

Quest of shape coexistence in Zr isotopes

Quest of shape coexistence in Zr isotopes

Shape phase transitions in odd-A Zr isotopes

Evolution of the phenomenologically determined collective potential along the chain of Zr isotopes

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