Effective field theories for collective excitations of atomic nuclei

Abstract

Collective modes emerge as the relevant degrees of freedom that govern low-energy excitations of atomic nuclei. These modes - rotations, pairing rotations, and vibrations - are separated in energy from non-collective excitations, making it possible to describe them in the framework of effective field theory. Rotations and pairing rotations are the remnants of Nambu-Goldstone modes from the emergent breaking of rotational symmetry and phase symmetries in finite deformed and finite superfluid nuclei, respectively. The symmetry breaking severely constrains the structure of low-energy Lagrangians and thereby clarifies what is essential and simplifies the description. The approach via effective field theories exposes the essence of nuclear collective excitations and is defined with a breakdown scale in mind. This permits one to make systematic improvements and to estimate and quantify uncertainties. Effective field theories of collective excitations have been used to compute spectra, transition rates, and other matrix elements of interest. In particular, predictions of the nuclear matrix element for neutrinoless double beta decay then come with quantified uncertainties. This review summarizes these results and also compares the approach via effective field theories to well-known models and ab initio computations.

arXiv comment84 pages, 23 figures

References in corpus (94)

• Modern Theory of Nuclear Forces
• Chiral effective field theory and nuclear forces
• The Shell Model as Unified View of Nuclear Structure
• Effective Field Theory for Few-Nucleon Systems
• Relativistic Nuclear Energy Density Functionals: Mean-Field and Beyond
• Status and Future of Nuclear Matrix Elements for Neutrinoless Double-Beta Decay: A Review
• Coupled-cluster computations of atomic nuclei
• Structure of even-even nuclei using a mapped collective Hamiltonian and the D1S Gogny interaction
• Nuclear effective field theory: status and perspectives
• Nuclear energy density optimization: Large deformations
• Disassembling the Nuclear Matrix Elements of the Neutrinoless double beta Decay
• Exactly solvable Richardson-Gaudin models for many-body quantum systems
• $0\nu \beta \beta$ and $2\nu \beta \beta$ nuclear matrix elements in the interacting boson model with isospin restoration
• Error Estimates of Theoretical Models: a Guide
• Structure and rotations of the Hoyle state
• Systematic study of deformed nuclei at the drip lines and beyond
• Global performance of covariant energy density functionals: ground state observables of even-even nuclei and the estimate of theoretical uncertainties
• Symmetry breaking and quantum correlations in finite systems: Studies of quantum dots and ultracold Bose gases and related nuclear and chemical methods
• Nonrelativistic effective Lagrangians
• Mean field and beyond description of nuclear structure with the Gogny force: A review
• Effective field theory description of halo nuclei
• Ab Initio Treatment of Collective Correlations and the Neutrinoless Double Beta Decay of ${}^{48}$Ca
• Spontaneous Symmetry Breaking and Nambu-Goldstone Bosons in Quantum Many-Body Systems
• Solutions of the Bohr hamiltonian, a compendium
• First observation of two-neutrino double electron capture in ${}^{124}$Xe with XENON1T
• Collective Modes in Light Nuclei from First Principles
• Symmetry restoration in mean-field approaches
• A recipe for EFT uncertainty quantification in nuclear physics
• Bayesian parameter estimation for effective field theories
• Meaningful characterisation of perturbative theoretical uncertainties
• Physics of nuclei: Key role of an emergent symmetry
• Quantified limits of the nuclear landscape
• Exploring Bayesian parameter estimation for chiral effective field theory using nucleon-nucleon phase shifts
• Ab initio neutrinoless double-beta decay matrix elements for 48Ca, 76Ge, and 82Se
• Nilsson-SU3 selfconsistency in heavy N=Z nuclei
• Neutrinoless $\beta \beta$ decay mediated by the exchange of light and heavy neutrinos: The role of nuclear structure correlations
• Double Gamow-Teller transitions and its relation to neutrinoless $\beta \beta$ decay
• Ab initio Bogoliubov coupled cluster theory for open-shell nuclei
• A computationally tractable version of the collective model
• Late time physics of holographic quantum chaos
• Symmetry Breaking and Finite Size Effects in Quantum Many-Body Systems
• Coupled-cluster calculations of neutrinoless double-beta decay in ${}^{48}$Ca
• Rigorous constraints on three-nucleon forces in chiral effective field theory from fast and accurate calculations of few-body observables
• Bayesian Methods for Parameter Estimation in Effective Field Theories
• Cooper pair transfer in nuclei
• Projected Coupled Cluster Theory
• On Gauge Invariance and Minimal Coupling
• Angular-momentum projection in coupled-cluster theory: structure of ${}^{34}$Mg
• Study of the transition from pairing vibrational to pairing rotational regimes between magic numbers N=50 and N=82, with two-nucleon transfer
• Spin-wave Scattering in the Effective Lagrangian Perspective
• Evidence for rigid triaxial deformation in ${}^{76}$Ge from a model-independent analysis
• Emergence of rotational bands in ab initio no-core configuration interaction calculations of the Be isotopes
• An extensive survey of the estimation of uncertainties from missing higher orders in perturbative calculations
• Effective field theory for nuclear vibrations with quantified uncertainties
• Ab initio uncertainty quantification of neutrinoless double-beta decay in ${}^{76}$Ge
• Symmetry energy in nuclear density functional theory
• Systematic Low-Energy Effective Theory for Magnons and Charge Carriers in an Antiferromagnet
• Effective Field Theory Approach to Ferromagnets and Antiferromagnets in Crystaline Solids
• Charge-symmetry breaking forces and isospin mixing in 8Be
• Double-Weak Decays of ${}^{124}$Xe and ${}^{136}$Xe in the XENON1T and XENONnT Experiments
• Effective Field Theory for Finite Systems with Spontaneously Broken Symmetry
• Emergence of rotational bands in ab initio no-core configuration interaction calculations of light nuclei
• Breaking and restoring symmetries within the nuclear energy density functional method
• Exact diagonalization of the Bohr Hamiltonian for rotational nuclei: Dynamical gamma softness and triaxiality
• Search for double-beta decay of 136Xe to excited states of 136Ba with the KamLAND-Zen experiment
• Effective theory for deformed nuclei
• Neutrinoless $\beta \beta$ decay nuclear matrix elements in an isotopic chain
• Pairing Nambu-Goldstone Modes within Nuclear Density Functional Theory
• Collective inertia of Nambu-Goldstone mode from linear response theory
• Particles in non-Abelian gauge potentials - Landau problem and insertion of non-Abelian flux
• Two-neutrino double electron capture on ${}^{124}$Xe based on an effective theory and the nuclear shell model
• Collective rotation from ab initio theory
• Towards heavy-mass ab initio nuclear structure: Open-shell Ca, Ni and Sn isotopes from Bogoliubov coupled-cluster theory
• Pions versus Magnons: From QCD to Antiferromagnets and Quantum Hall Ferromagnets
• Multiscale physics of atomic nuclei from first principles
• Ab initio computations of strongly deformed nuclei around ${}^{80}$Zr
• Effective theory for the non-rigid rotor in an electromagnetic field: Toward accurate and precise calculations of E2 transitions in deformed nuclei
• Neutrinoless double-beta decay from an effective field theory for heavy nuclei
• Gamow-Teller and double-beta decays of heavy nuclei within an effective theory
• Search for $2\nu \beta \beta$ decay of ${}^{136}$Xe to the 0${}_1^{+}$ excited state of ${}^{136}$Ba with EXO-200
• Effective field theory for triaxially deformed nuclei
• Rotor Spectra, Berry Phases, and Monopole Fields: from Antiferromagnets to QCD
• Effective Field Theory of Emergent Symmetry Breaking in Deformed Atomic Nuclei
• Effective field theory for vibrations in odd-mass nuclei
• Ab initio computations from ${}^{78}$Ni towards ${}^{70}$Ca along neutron number $N=50$
• Effective field theory for deformed odd-mass nuclei
• Rotational constants of multi-phonon bands in an effective theory for deformed nuclei
• E2 Rotational Invariants of $0_1^{+}$ and $2_1^{+}$ states for ${}^{106}$Cd: the Emergence of Collective Rotation
• Two-neutrino $\beta \beta$ decay of ${}^{136}$Xe to the first excited $0^{+}$ state in ${}^{136}$Ba
• Effective field theory of pairing rotations
• From bare to renormalized order parameter in gauge space: structure and reactions
• Quantum-number projected generator coordinate method for ${}^{21}$Ne with a chiral two-nucleon-plus-three-nucleon interaction
• Extending pairing energy density functional using pairing rotational moments of inertia
• Effective field theory for collective rotations and vibrations of triaxially deformed nuclei

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