Generator coordinate method for nuclear octupole excitations: status and perspectives

Abstract

Strong octupole correlations have been observed in the low-lying states of atomic nuclei across various mass regions. In this review, we provide an overview of Beyond Mean-Field (BMF) studies of nuclear octupole collective motions with Generator Coordinate Method (GCM) in combination with quantum-number projections that are implemented to restore the broken symmetries in nuclear mean-field states. We highlight recent developments within this framework and their applications to excitation spectra and electromagnetic transition rates in octupole-shaped nuclei and hypernuclei. We discuss the novel phenomena of nucleon clustering in light nuclei. Additionally, we explore the phase transition from octupole vibrations to rotational motions as spin increases in heavy nuclei. Lastly, we examine the status and future prospects of studies on octupole deformation effects in nuclear Schiff moments. These studies, along with the upper limits of atomic Electric Dipole Moment (EDM), impose stringent constraints on beyond-standard-model time-reversal-violating nucleon-nucleon interactions.

arXiv comment56 pages, 21 figures, an invited review for the journal Int. J. Mod. Phys. E

References in corpus (104)

• Relativistic Continuum Hartree Bogoliubov Theory for Ground State Properties of Exotic Nuclei
• A program for coupled-channels calculations with all order couplings for heavy-ion fusion reactions
• Electroweak baryogenesis
• New parametrization for the nuclear covariant energy density functional with point-coupling interaction
• Relativistic Nuclear Energy Density Functionals: Mean-Field and Beyond
• Electric Dipole Moments of Nucleons, Nuclei, and Atoms: The Standard Model and Beyond
• From low-momentum interactions to nuclear structure
• The In-Medium Similarity Renormalization Group: A Novel Ab Initio Method for Nuclei
• Electric Dipole Moments of the Atoms, Molecules, Nuclei and Particles
• Ab initio calculation of the Hoyle state
• Subbarrier fusion reactions and many-particle quantum tunneling
• Microscopic Clustering in Light Nuclei
• A finite range pairing force for density functional theory in superfluid nuclei
• Structure and rotations of the Hoyle state
• A Guided Tour of Ab Initio Nuclear Many-Body Theory
• Enhanced T-odd P-odd Electromagnetic Moments in Reflection Asymmetric Nuclei
• Structure of ground and excited states of ${}^{12}$C
• Molecular Dynamics for Fermions
• Nuclear time-reversal violation and the Schiff moment of 225Ra
• Coupled-channels analysis of the ${}^{16}$O+${}^{208}$Pb fusion barrier distribution
• Mean field and beyond description of nuclear structure with the Gogny force: A review
• Potential Energy Surfaces of Actinide Nuclei from a Multi-dimensional Constraint Covariant Density Functional Theory: Barrier Heights and Saddle Point Shapes
• Ab Initio Treatment of Collective Correlations and the Neutrinoless Double Beta Decay of ${}^{48}$Ca
• Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics
• Direct Evidence of Octupole Deformation in Neutron-Rich ${}^{144}$Ba
• Collective T- and P- Odd Electromagnetic Moments in Nuclei with Octupole Deformations
• Fission barriers in covariant density functional theory: extrapolation to superheavy nuclei
• Cluster structures within Fermionic Molecular Dynamics
• Particle-Number Restoration within the Energy Density Functional Formalism
• Octupole deformation in the ground states of even-even nuclei: a global analysis within the covariant density functional theory
• Electric dipole moments of Hg, Xe, Rn, Ra, Pu, and TlF induced by the nuclear Schiff moment and limits on time-reversal violating interactions
• Particle-Number Restoration within the Energy Density Functional formalism: Nonviability of terms depending on noninteger powers of the density matrices
• Deformed Base Antisymmetrized Molecular Dynamics and its Application to ^{20}Ne
• Symmetry restoration in mean-field approaches
• Time-Reversal Violating Schiff Moment of 225Ra
• Beyond Mean-Field Calculations for Odd-A Nuclei
• Direct Evidence for Octupole Deformation in ${}^{146}$Ba and the Origin of Large $E1$ Moment Variations in Reflection-Asymmetric Nuclei
• Rod-shaped Nuclei at Extreme Spin and Isospin
• Improved limit on the ${}^{225}$Ra electric dipole moment
• Evidence of quadrupole and octupole deformations in ${}^{96}$Zr+${}^{96}$Zr and ${}^{96}$Ru+${}^{96}$Ru collisions at ultra-relativistic energies
• Get on the BAND Wagon: A Bayesian Framework for Quantifying Model Uncertainties in Nuclear Dynamics
• Evolution of Octupole Deformation in Radium Nuclei from Coulomb Excitation of Radioactive ${}^{222}$Ra and ${}^{228}$Ra Beams
• New Limit on the Permanent Electric Dipole Moment of ${}^{129}$Xe using ${}^3$He Comagnetometry and SQUID Detection
• Linear chain structure of four-$\alpha$ clusters in ${}^{16}$O
• Landscape of pear-shaped even-even nuclei
• Alpha-Particle Clustering from Expanding Self-Conjugate Nuclei within the Hartree-Fock-Bogoliubov Approach
• Fully self-consistent calculations of nuclear Schiff moments
• Calculation of P,T-odd electric dipole moments for diamagnetic atoms ${}^{129}$Xe, ${}^{171}$Yb, ${}^{199}$Hg, ${}^{211}$Rn, and ${}^{225}$Ra
• Evidence of the triaxial structure of ${}^{129}$Xe at the Large Hadron Collider
• Simultaneous quadrupole and octupole shape phase transitions in Thorium
• P- and T-violating Schiff moment of the Mercury nucleus
• Nuclear Octupole Correlations and the Enhancement of Atomic Time-Reversal Violation
• Hoyle band and $\alpha$ condensation in ${}^{12}\mathrm{C}$
• Multi-reference many-body perturbation theory for nuclei III -- Ab initio calculations at second order in PGCM-PT
• Spectroscopy of quadrupole and octupole states in rare-earth nuclei from a Gogny force
• Correlating Schiff moments in the light actinides with octupole moments
• Emergent geometry and duality in the carbon nucleus
• Microscopic description of quadrupole-octupole coupling in Sm and Gd isotopes with the Gogny Energy Density Functional
• Time-Reversal-Violating Schiff Moment of 199Hg
• Spectroscopy of reflection-asymmetric nuclei with relativistic energy density functionals
• Beyond relativistic mean-field approach for nuclear octupole excitations
• Beyond-mean-field approaches for nuclear neutrinoless double beta decay in the standard mechanism
• Anatomy of molecular structures in ${}^{20}$Ne
• Reflection asymmetric relativistic mean field approach and its application to the octupole deformed nucleus ${}^{226}$Ra
• The Time-Reversal- and Parity-Violating Nuclear Potential in Chiral Effective Theory
• Octupole deformation in the nuclear chart based on the 3D Skyrme Hartree-Fock plus BCS model
• Multiple chiral doublet bands with octupole correlations in reflection-asymmetric triaxial particle rotor model
• Quadrupole and octupole collectivity and cluster structures in neon isotopes
• Electric dipole moments of atoms and molecules produced by enhanced nuclear Schiff moments
• Localization and clustering in the nuclear Fermi liquid
• Octupole degree of freedom for the critical-point candidate nucleus ${}^{152}$Sm in a reflection-asymmetric relativistic mean-field approach
• Relativistic Normal Coupled-Cluster Theory for Accurate Determination of Electric Dipole Moments of Atoms: First application to ${}^{199}$Hg atom
• Improved limits on the hadronic and semi-hadronic CP violating parameters and role of a dark force carrier in the electric dipole moment of ${}^{199}$Hg
• Enhancement of nuclear Schiff moments and time reversal violation in atoms due to soft nuclear octupole vibrations
• New Constraint of Clustering for AMD and Its Application to the Study of $2\alpha$-${}^{12}$C Structure of ${}^{20}$Ne
• GCM Analysis of the collective properties of lead isotopes with exact projection on particle numbers
• Effects of core polarization on the nuclear Schiff moment
• Deformation and cluster structures in ${}^{12}$C studied with configuration mixing using Skyrme interactions
• Modification of triaxial deformation and change of spectrum in ${}_{\Lambda }^{25}$Mg caused by $\Lambda$ hyperon
• Searching for 4$\alpha$ linear-chain structure in excited states of ${}^{16}$O with a covariant density functional theory
• Beyond mean-field study of elastic and inelastic electron scattering off nuclei
• Octupole correlations in low-lying states of 150Nd and 150Sm and their impact on neutrinoless double-beta decay
• Anatomy of octupole correlations in ${}^{96}$Zr with a symmetry-restored multidimensionally-constrained covariant density functional theory
• Nuclear Schiff moment in nuclei with soft octupole and quadrupole vibrations
• Ground-state properties of even and odd Magnesium isotopes in a symmetry-conserving approach
• Cluster structures in ${}^{12}$C from global energy density functionals
• Enhanced nuclear Schiff moment in stable and metastable nuclei
• Microscopic origin of reflection-asymmetric nuclear shapes
• Generator coordinate method for hypernuclear spectroscopy with a covariant density functional
• Large-scale shell-model calculations of nuclear Schiff moments of ${}^{129}$Xe and ${}^{199}$Hg
• Angular momentum and parity projected multidimensionally constrained relativistic Hartree-Bogoliubov model
• Electric dipole moment of ${}^{225}$Ra due to P- and T-violating weak interactions
• Iterative approaches to the self-consistent nuclear energy density functional problem. Heavy ball dynamics and potential preconditioning
• Anharmonicity of multi-octupole-phonon excitations in ${}^{208}$Pb: analysis with multi-reference covariant density functional theory and subbarrier fusion of ${}^{16}$O+${}^{208}$Pb
• Ab initio calculations of electric dipole moments of light nuclei
• Application of efficient generator-coordinate subspace-selection algorithm to neutrinoless double-$\beta$ decay
• Optimization of generator coordinate method with machine-learning techniques for nuclear spectra and neutrinoless double-beta decay: ridge regression for nuclei with axial deformation
• Beyond mean-field approach for pear-shaped hypernuclei
• Electric dipole moments of superheavy elements - A case study on copernicium
• Enhancement of octupole strength in near spherical nuclei
• Origin of octupole deformation softness in atomic nuclei
• The interplay of single-particle and collective motions in the low-lying states of ${}_{\Lambda }^{21}$Ne with quadrupole-octupole correlations
• Visualization of nuclear many-body correlations with the most probable configuration of nucleons
• Symmetry restoration methods

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