Shape coexistence in even-even nuclei: A theoretical overview

Abstract

The last decade has seen a rapid growth of our understanding of the microscopic origins of shape coexistence, assisted by the new data provided by the modern radioactive ion beam facilities built worldwide. Islands of the nuclear chart in which shape coexistence can occur have been identified, and the different microscopic particle-hole excitation mechanisms leading to neutron-induced or proton-induced shape coexistence have been clarified. The relation of shape coexistence to the islands of inversion, appearing in light nuclei, to the new spin-aligned phase appearing in N=Z nuclei, as well as to shape/phase transitions occurring in medium mass and heavy nuclei, has been understood. In the present review, these developments are considered within the shell model and mean field approaches, as well as by symmetry methods. In addition, based on systematics of data, as well as on symmetry considerations, quantitative rules are developed, predicting regions in which shape coexistence can appear, as a possible guide for further experimental efforts, which can help in improving our understanding of the details of the nucleon-nucleon interaction, as well as of its modifications occurring far from stability.

80 pages, 14 figures, 837 references

References in corpus (80)

• DIRHB -- a relativistic self-consistent mean-field framework for atomic nuclei
• Quantum phase transitions in the interacting boson model
• Beyond the relativistic mean-field approximation (III): collective Hamiltonian in five dimensions
• Overview of Neutron-Proton Pairing
• Evidence for a spin-aligned neutron-proton paired phase from the level structure of ${}^{92}$Pd
• Discovery of the shape coexisting 0+ state in 32Mg by a two neutron transfer reaction
• Symmetry-guided large-scale shell-model theory
• Shape coexistence in neutron-deficient Kr isotopes: Constraints on the single-particle spectrum of self-consistent mean-field models from collective excitations
• Observation of isotonic symmetry for enhanced quadrupole collectivity in neutron-rich 62,64,66Fe isotopes at N=40
• Status of Alpha-Particle Condensate Structure of the Hoyle State
• First Measurement of Collectivity of Coexisting Shapes based on Type II Shell Evolution: The Case of ${}^{96}$Zr
• Microscopic description of nuclear quantum phase transitions
• Shape transitions in neutron-rich Yb, Hf, W, Os, and Pt isotopes within a Skyrme Hartree-Fock + BCS approach
• Evidence for Symplectic Symmetry in Ab Initio No-Core Shell Model Results for Light Nuclei
• Beyond the relativistic mean-field approximation (II): configuration mixing of mean-field wave functions projected on angular momentum and particle number
• Structural evolution in $A\approx 100$ nuclei within the mapped interacting boson model based on the Gogny energy density functional
• Microscopic Formulation of Interacting Boson Model for Rotational Nuclei
• Axially deformed relativistic Hartree Bogoliubov with separable pairing force
• Analytic predictions for nuclear shapes, the prolate dominance and the prolate-oblate shape transition in the proxy-SU(3) model
• Proxy-SU(3) symmetry in heavy deformed nuclei
• Global study of beyond-mean-field correlation energies in covariant energy density functional theory using a collective Hamiltonian method
• Unveiling the intruder deformed 0${}_2^{+}$ state in ${}^{34}$Si
• Energy Density Functional analysis of shape evolution in N=28 isotones
• Empirical Proton-Neutron Interactions and Nuclear Density Functional Theory: Global, Regional and Local Comparisons
• Structure of Krypton isotopes calculated with symmetry conserving configuration mixing methods
• Structural evolution in Pt isotopes with the Interacting Boson Model Hamiltonian derived from the Gogny Energy Density Functional
• Nuclear Dynamics and Reactions in the Ab Initio Symmetry-Adapted Framework
• Microscopic description of oblate-prolate shape mixing in proton-rich Se isotopes
• Phase transition in exotic nuclei along the $N=Z$ line
• Search for Intrinsic Excitations in 152Sm
• The islands of shape coexistence within the Elliott and the proxy-SU(3) Models
• Spin-aligned neutron-proton pairs in $N=Z$ nuclei
• E(5) and X(5) shape phase transitions within a Skyrme Hartree-Fock + BCS approach
• Intertwined Quantum Phase Transitions in the Zr Isotopes
• Shape mixing dynamics in the low-lying states of proton-rich Kr isotopes
• Nature of isomerism in exotic sulfur isotopes
• Evidence for coexisting shapes in ${}^{98}$Zr through lifetime measurements
• Discovery of a new isomeric state in ${}^{68}$Ni: Evidence for a highly-deformed proton intruder state
• Shape coexistence in Lead isotopes in the interacting boson model with Gogny energy density functional
• Triaxiality and shape coexistence in Germanium isotopes
• A beyond mean field analysis of the shape transition in the Neodymium isotopes
• Zr Isotopes as a region of intertwined quantum phase transitions
• Diversity of shapes and rotations in the gamma-soft 130Ba nucleus: first observation of a t-band in the A=130 mass region
• N=90 region: The decays of {152m,g}Eu to 152Sm
• Shape changes in the mirror nuclei ${}^{70}$Kr and ${}^{70}$Se
• Emergent symplectic symmetry in atomic nuclei: Ab initio symmetry-adapted no-core shell model
• Shape coexistence and neutron skin thickness of Pb isotopes by the deformed relativistic Hartree-Bogoliubov theory in continuum
• The subtle connection between shape coexistence and quantum phase transition. The Zr case
• Isoscalar and isovector pairing in a formalism of quartets
• Global analysis of quadrupole shape invariants based on covariant energy density functionals
• Bubble nuclei with shape coexistence in even-even isotopes of Hf to Hg
• Shape changes and large-amplitude collective dynamics in neutron-rich Cr isotopes
• Prolate over oblate dominance in deformed nuclei as a consequence of the SU(3) symmetry and the Pauli principle
• Variational procedure for nuclear shell-model calculations and energy-variance extrapolation
• Shape Coexistence at Zero Spin in 64Ni Driven by the Monopole Tensor Interaction
• Triaxial quadrupole deformation dynamics in sd-shell nuclei around 26Mg
• Why nuclear forces favor the highest weight irreducible representations of the fermionic SU(3) symmetry
• Proton-neutron pairing vibrations in N=Z nuclei: Precursory soft mode of isoscalar pairing condensation
• Structure of krypton isotopes within the interacting boson model derived from the Gogny energy density functional
• What can be learned from binding energy differences about nuclear structure: the example of delta V_{pn}
• Quadrupole Collective Dynamics from Energy Density Functionals: Collective Hamiltonian and the Interacting Boson Model
• Shape coexistence revealed in the $N=Z$ isotope ${}^{72}$Kr through inelastic scattering
• Configuration mixing in the neutron-deficient ${}^{186-196}$Pb isotopes
• Euclidean Dynamical Symmetry in Nuclear Shape Phase Transitions
• Description of shape coexistence in ${}^{96}$Zr based on the collective quadrupole Bohr Hamiltonian
• Mapping the $N=40$ Island of Inversion: Precision Mass Measurements of Neutron-rich Fe Isotopes
• First Evidence of Axial Shape Asymmetry and Configuration Coexistence in ${}^{74}$Zn: Suggestion for a Northern Extension of the $N=40$ Island of Inversion
• Shape coexistence in Sr isotopes
• Direct probing of the cluster structure in ${}^{12}$Be via $\alpha$-knockout reaction
• Coherence features of the spin-aligned neutron-proton pair coupling scheme
• Large enhancement of total reaction cross sections at the edge of the island of inversion in Ti, Cr, and Fe isotopes
• Partial dynamical symmetries and shape coexistence in nuclei
• Conformable Fractional Bohr Hamiltonian with Bonatsos and Double-Well Sextic Potentials
• Description of the low-lying collective states of ${}^{96}$Zr based on the quadrupole-collective Bohr Hamiltonian
• Transition probabilities in the X(5) candidate ${}^{122}$Ba
• E2 Rotational Invariants of $0_1^{+}$ and $2_1^{+}$ states for ${}^{106}$Cd: the Emergence of Collective Rotation
• Triaxial nuclei and analytical solutions of the conformable fractional Bohr Hamiltonian with some exponential-type potentials
• Study of shape transitions in $N\sim 90$ isotopes with beyond mean field calculations
• Low energy 0+ excitations in 158Gd
• Quenching of N = 28 shell gap and a low-lying quadrupole mode in the vicinity of neutron-rich N = 28 isotones