The Shell Model as Unified View of Nuclear Structure

Abstract

The last decade has witnessed both quantitative and qualitative progresses in Shell Model studies, which have resulted in remarkable gains in our understanding of the structure of the nucleus. Indeed, it is now possible to diagonalize matrices in determinantal spaces of dimensionality up to 10^9 using the Lanczos tridiagonal construction, whose formal and numerical aspects we will analyze. Besides, many new approximation methods have been developed in order to overcome the dimensionality limitations. Furthermore, new effective nucleon-nucleon interactions have been constructed that contain both two and three-body contributions. The former are derived from realistic potentials (i.e., consistent with two nucleon data). The latter incorporate the pure monopole terms necessary to correct the bad saturation and shell-formation properties of the realistic two-body forces. This combination appears to solve a number of hitherto puzzling problems. In the present review we will concentrate on those results which illustrate the global features of the approach: the universality of the effective interaction and the capacity of the Shell Model to describe simultaneously all the manifestations of the nuclear dynamics either of single particle or collective nature. We will also treat in some detail the problems associated with rotational motion, the origin of quenching of the Gamow Teller transitions, the double beta-decays, the effect of isospin non conserving nuclear forces, and the specificities of the very neutron rich nuclei. Many other calculations--that appear to have ``merely'' spectroscopic interest--are touched upon briefly, although we are fully aware that much of the credibility of the Shell Model rests on them.

64 pages, 60 figures

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• Prolate-to-oblate shape phase transitions in neutron-rich odd-mass nuclei
• Transition sum rules in the shell model
• Effective interactions and large-scale diagonalization for quantum dots
• Configuration mixing and intertwined quantum phase transitions in odd-mass niobium isotopes
• Detection prospects for the second-order weak decays of ${}^{124}$Xe in multi-tonne xenon time projection chambers
• Microscopic study of neutron-rich Dysprosium isotopes
• Prolate-oblate asymmetric shape phase transition in the interacting boson model with SU (3) higher-order interactions
• Broken mirror symmetry in ${}^{36}$S and ${}^{36}$Ca
• Complex valence-space effective operators for observables: the Gamow-Teller transition
• Shell-model study of spectroscopies and isospin structures in odd-odd $N=Z$ nuclei employing realistic \emph{NN} potentials
• Ab initio no-core shell model description of ${}^{10-14}$C isotopes
• Non-parametric Bayesian approach to extrapolation problems in configuration interaction methods
• Variation after projection calculations for high-spin states
• $\beta$-decay rates of ${}^{(115,117)}$Rh into ${}^{(115,117)}$Pd isotopes in the microscopic IBFM-2
• The nucleon-pair approximation for nuclei from spherical to deformed regions
• Screening Effects on Electron Capture Rates and Type Ia Supernova Nucleosynthesis
• Neutrinoless double beta decay rates in the presence of light sterile neutrinos
• Ab initio coupled-cluster and configuration interaction calculations for 16-O using V_UCOM
• Nuclear states projected from a pair condensate
• Neutron-proton pairing and double-beta decay in the interacting boson model
• Shell-model phenomenology of low-momentum interactions
• Investigation of spectroscopic factors of deeply-bound nucleons in drip-line nuclei with the Gamow shell model
• Global Properties of fp-Shell Interactions in Many-nucleon Systems
• Spectroscopy of odd-odd nuclei within the interacting boson-fermion-fermion model based on the Gogny energy density functional
• Quantum computation algorithm for many-body studies
• Neutrinoless $\beta \beta$ decay nuclear matrix elements complete up to N${}^2$LO in heavy nuclei
• Sensitivity of quasi-free reactions on details of the bound-state overlap functions
• Finite-temperature linear response theory based on relativistic Hartree Bogoliubov model with point-coupling interaction
• The structure of low-lying states in ${}^{140}$Sm studied by Coulomb excitation
• Sensitivity of Carbon and Oxygen Yields to the Triple-Alpha Resonance in Massive Stars
• Neutrinoless double-$\beta$ decay and double Gamow-Teller transitions
• Present Status of Nuclear Shell-Model Calculations of Neutrinoless Double-Beta Decay Matrix Elements
• The quark mean field model with pion and gluon corrections
• Role of quadrupole deformation and continuum effects in the "island of inversion'' nuclei ${}^{28,29,31}$F
• Interplay between pairing and triaxial shape degrees of freedom in Os and Pt nuclei
• Effective shell-model interaction for nuclei southeast of ${}^{100}$Sn
• Double Beta Decay APPEC Committee Report
• Gamow-Teller response in the configuration space of DFT-rooted no-core configuration-interaction model
• One-neutron halo structure of ${}^{29}$Ne
• Comparison of shell model results for even-even Se isotopes
• Shell model analysis of the $B(E2,2^{+}\to 0^{+})$'s in the A=70 T=1 triplet
• Decay widths at the scission point in nuclear fission
• The role of the g9/2 orbital in the development of collectivity in the A = 60 region: The case of 61Co
• Shell Model and Mean-Field Description of Band Termination
• Core-polarization effects and effective charges in O and Ni isotopes from chiral interactions
• Inelastic nuclear scattering from neutrinos and dark matter
• Generalized Seniority on Deformed Single-Particle Basis
• Benchmarking projected Hartree-Fock as an approximation
• Role of momentum transfer in the quenching of Gamow-Teller strength
• The Cranked Nilsson-Strutinsky versus the Spherical Shell Model: A Comparative Study of pf-Shell Nuclei
• Nucleon-pair coupling scheme in Elliott's SU(3) model
• Properties of infrared extrapolations in a harmonic oscillator basis
• A Constrained-Path Quantum Monte-Carlo Approach for the Nuclear Shell Model
• Nuclear structure study with core excitations in Ni region: for $fp{g}_{9/2}$ space
• Array of Cryogenic Calorimeters to Evaluate the Spectral Shape of forbidden $\beta$-decays: the ACCESS project
• Measurement-efficient quantum Krylov subspace diagonalisation
• Nucleon-pair truncation of the shell model for medium-heavy nuclei
• Two-neutrino double-beta decay matrix elements based on relativistic nuclear energy density functional
• Probabilistic chain teleportation of a qutrit-state
• Gamma-ray spectroscopy of ${}_{17}^{38}$Cl using grazing reactions
• Bound-State Beta Decay of ${}^{205}{\mathrm{Tl}}^{81+}$ Ions and the LOREX Project
• Particle-Number Projected Hartree-Fock-Bogoliubov Study with Effective Shell Model Interactions
• Configuration interaction projected density functional theory: effects of four-quasiparticle configurations and time-odd interactions
• Low-energy structure and $\beta$ decay properties of neutron-rich nuclei in the region of a shape phase transition
• Shell-model results in $fp$ and $fp{g}_{9/2}$ spaces for ${}^{61,63,65}$Co isotopes
• Study of Gamow-Teller transitions in isotopes of titanium within the quasi particle random phase approximation
• Ab-initio no-core shell model study of ${}^{18-24}$Ne isotopes
• From the liquid drop model to lattice QCD
• Higgs shifts from electron-positron annihilations near neutron stars
• Low-lying 2${}^{+}$ states generated by $pn$-quadrupole correlation and $N=28$ shell quenching
• Summation of Parquet diagrams as an ab initio method in nuclear structure calculations
• A modified Brink-Axel hypothesis for astrophysical Gamow-Teller transitions
• The spectra of mixed ${}^3$He-${}^4$He droplets
• Ingredients of nuclear matrix element for two-neutrino double-beta decay of 48Ca
• Comparison of Gamow-Teller strengths in the random phase approximation
• Gamow-Teller properties of the double beta-decay partners 116Cd(Sn) and 150Nd(Sm)
• Advancing quantum simulations of nuclear shell model with noise-resilient protocols
• Charge-exchange reaction cross sections and the Gamow-Teller strength for double beta decay
• Variational Monte Carlo method for shell-model calculations in odd-mass nuclei and restoration of symmetry
• No-core shell model for 48-Ca, 48-Sc and 48-Ti
• Initialization effects of nucleon profile on the $\pi$ yields in heavy-ion collisions at medium energies
• Rotational bands beyond the Elliott model
• Radii in the $sd$ shell and the $s_{1/2}$ "halo" orbit: A game changer
• Single-particle and collective structures in neutron-rich Sr isotopes
• Signatures of shape phase transitions in krypton isotopes based on relativistic energy density functionals
• Quasidynamical symmetries in the backbending of chromium isotopes
• Two-neutrino $\beta \beta$ decay of ${}^{136}$Xe to the first excited $0^{+}$ state in ${}^{136}$Ba
• Gamow-Teller transitions of neutron-rich $N=82,81$ nuclei by shell-model calculations
• Ab initio nuclear shape coexistence and emergence of island of inversion around $N=20$
• Ab initio no-core shell model study of neutron-rich ${}^{18,19,20}$C isotopes
• Probing proton cross-shell excitations through the two-neutron removal from 38Ca
• Effective field theory and inelastic dark matter results from XENON1T
• Global performance of multireference density functional theory for low-lying states in $sd$-shell nuclei
• Benchmark of many-body approaches for magnetic dipole transition strength
• The role of low-lying resonances for ${}^{10}$Be(p,$\alpha$) reaction rate and implications for the formation of the Solar System
• Structure of ${}^{43}$P and ${}^{42}$Si in a two-level shape-coexistence model
• Simultaneous description of $\beta$ decay and low-lying structure of neutron-rich even- and odd-mass Rh and Pd nuclei
• Uncertainty quantification for $\mu \to e$ conversion in nuclei: charge distributions
• High-spin structure in ${}^{40}$K
• Nuclear structure study around Z=28
• Astrophysics in 2005
• Exact sum rules with approximate ground states
• Shell model description of Ge isotopes
• Border of the Island of Inversion: Unbound states in ${}^{29}$Ne
• Nuclear Schiff Moments and CP Violation
• Combined few-body and mean-field model for nuclei
• Configuration interaction relativistic Hartree-Fock model
• Quadrupole properties of the eight $SU(3)$ algebras in $(sdgi)$ space
• Recent developments in the shell model Monte Carlo approach to nuclei
• Shell model results for $T=1$ and $T=0$ bands in ${}^{66}$As
• Perspectives on few-body cluster structures in exotic nuclei
• Fast-timing study of ${}^{81}$Ga from the $\beta$ decay of ${}^{81}$Zn
• Realistic shell-model calculations: current status and open problems
• Structure of odd Ge isotopes with $40<N<50$
• Shell model study of the pairing correlations
• Neutrinos from pre-supernova in the framework of TQRPA method
• Different seniority states of ${}^{119-126}$Sn isotopes: shell model description
• Simultaneous Measurement of Half-Life and Spectral Shape of ${}^{115}$In $\beta$-decay with an Indium Iodide Cryogenic Calorimeter
• Electric and magnetic dipole strength in ${}^{58}$Ni from forward-angle inelastic proton scattering
• Is it possible to study neutrinoless $\beta \beta$ decay by measuring double Gamow-Teller transitions?
• A Quantum Annealing Protocol to Solve the Nuclear Shell Model
• Radiative and exchange corrections for two-neutrino double-beta decay
• Ab initio calculations of overlap integrals for $\mu \to e$ conversion in nuclei
• Artificial Intelligence Supported Shell-Model Calculations for Light Sn Isotopes
• Nuclear structure calculations for two-neutrino double-beta decay
• Forbidden electron capture on ${}^{24}$Na and ${}^{27}$Al in degenerate oxygen-neon cores
• Microscopic mass estimations
• Parameter dependence of the $\beta$-decay properties of neutron-rich Zr isotopes within the interacting boson model
• Nucleon momentum gap in asymmetric nuclear matter
• Probing effective nucleon-nucleon interaction at band termination
• A Vision for the Science of Rare Isotopes
• Double Beta Decay Experiments at Canfranc Underground Laboratory
• Gamow-Teller transitions and neutron-proton-pair transfer reactions
• Validity of Brink Axel Hypothesis for calculations of allowed stellar weak rates of heavy nuclei
• Monopole and Seniority Truncations in the Large-Scale Configuration Interaction Shell Model Approach
• Cross-shell excitations in doubly magic 132Sn and its nearest neighbours
• Persistence of the $Z=28$ shell gap in $A=75$ isobars: Identification of a possible $(1/2^{-})$ $\mu$s isomer in ${}^{75}$Co and $\beta$ decay to ${}^{75}$Ni
• Evolution of $N=28$ shell closure in relativistic continuum Hartree-Bogoliubov theory
• Testing the spin-cutoff parameterization with shell-model calculations
• Relativistic mean field study of 'islands of inversion' in neutron rich Z = 17 - 23, 37 - 40 and 60 - 64 nuclei
• Probing the Scalar WIMP-Pion Coupling with the first LUX-ZEPLIN data
• Multipole responses in fissioning nuclei and their uncertainties
• On the calculation and use of effective single-particle energies. The example of the neutron $1d_{3/2}$-$1d_{5/2}$ splitting along $\text{N}=20$ isotones
• Analytical evaluation of atomic form factors: application to Rayleigh scattering
• Model space truncation in shell-model fits
• Neutrino-nucleus interactions at low energies within Fermi-liquid theory
• Can we use heavy nuclei to detect relic neutrinos?
• Two-photon processes based on quantum commutators
• Revealing the nature of yrast states in neutron-rich polonium isotopes
• Nuclear structure properties of ${}^{193-200}$Hg isotopes within large-scale shell model calculations
• High-spin structures of ${}^{86,87,88,89}$Y: a shell model interpretation
• Isomeric states in neutron-rich nuclei around $N=40$
• Sensitivity analysis of random two-body interactions
• Systematic shell-model study of ${}^{98-130}$Cd isotopes and $8^{+}$ isomeric states
• Electric dipole response of sd-shell nuclei within the Configuration-Interaction Shell Model approach
• Towards Reliable Nuclear Matrix Elements for Neutrinoless $\beta \beta$ Decay
• Quantum self-organization and nuclear collectivities
• Shell model for heavy nuclei and its application in nuclear astrophysics
• New isomeric transition in ${}^{36}$Mg: Bridging the N=20 and N=28 islands of inversion
• Mixing of one-particle-one-hole projected states with the variation after projection wave functions
• Microscopic study of low-lying energy levels and electromagnetic properties in even-even ${}^{168-178}$Yb nuclei
• Effective field theories for collective excitations of atomic nuclei
• A Time Dependent Multi-Determinant approach to nuclear dynamics
• High-spin structures of ${}^{77,79,81,83}$As isotopes
• Study of shape coexistence in the 180-190Hg isotopes by SO(6) representation of eigenstates
• Ab initio nuclear structure via quantum adiabatic algorithm
• Revisiting the variational two-particle reduced density matrix for nuclear systems
• No-core shell model for A = 47 and A = 49
• Shell-model study for allowed and forbidden ${\beta }^{-}$ decay properties in the mass region "south" of ${}^{208}$Pb
• Deformation, halo, and bubble structure: A paradigm shift of exotic phenomena in light to medium mass nuclei
• NuLattice: Ab initio computations of atomic nuclei on lattices
• Structure of odd ${}^{79,81,83}$Se isotopes with proton and neutron excitations across $Z=28$ AND $N=40$
• Precision measurement of the ${}^{43}$Ca${}^{+}$ nuclear magnetic moment
• Theoretical description of nuclear collective excitations
• Toward scalable quantum computations of atomic nuclei
• Microscopic calculation of the ${\beta }^{-}$ decays of ${}^{151}$Sm, ${}^{171}$Tm, and ${}^{210}$Pb with implications to detection of the cosmic neutrino background
• Spurious dipole mode in random-phase approximation and in the RPA-based models
• Shell model study of high-spin states and band terminations in ${}^{67}$As
• Modern topics in theoretical nuclear physics
• Sensitivity analysis of $\beta$-decay half-life predictions for Ge, As, Zr and Mo nuclei within the mapped interacting boson model
• Axially Deformed Proton-Neutron Relativistic Quasiparticle Finite Amplitude Method for Charge-Exchange Transitions
• Modeling Ultra-High-Energy Cosmic Rays propagation using the input from Configuration Interaction Shell Model
• A way forward towards improvement of tensor force in \textit{pf}-shell
• Discrete non-orthogonal shell model for nuclear structure: Towards heavy elements
• Large scale shell model calculation for collectivity in nuclei beyond 78Ni
• A glimpse into an effective world
• Complex-scaled no-core shell model calculations of bound and unbound nuclear states in light nuclei
• Shell-model study of $\log ft$ values for ${}^{139,140,141}$Ba $\to$ ${}^{139,140,141}$La transitions
• A Semi-Empirical Formula for Two-Neutrino Double-Beta Decay
• Constrained-Path Quantum Monte-Carlo Approach for Non-Yrast States Within the Shell Model
• Forging the Link between Nuclear Reactions and Nuclear Structure
• Algebraic Gorkov solution in finite systems for the separable pairing interaction
• Bootstrapped Block Lanczos for large-dimension eigenvalue problems
• Symmetry energies for $A=24$ and $48$ and the USD and KB3 shell model Hamiltonians
• Two-neutrino $\beta \beta$ decay to excited states at next-to-leading order
• Exact solutions of the nuclear shell-model secular problem: Discrete Non-Orthogonal Shell Model within a Variation After Projection approach
• Ab initio calculations of beta-decay half-lives for $N=50$ neutron-rich nuclei
• Nucleon Electric Dipole Moments in Paramagnetic Molecules through Effective Field Theory
• Benchmarking projected generator coordinate method for nuclear Gamow-Teller transitions
• Nuclear level densities and $\gamma$-ray strength functions of ${}^{87}\mathrm{Kr}$ -- First application of the Oslo Method in inverse kinematics
• Broken Pair Model: A viable Alterative to the Shell Model for Odd-Spherical Nuclei
• ${}^{42}$Ca and ${}^{50}$Ca with the (Many- and Few-body) Unified Method
• Towards shell model interactions with credible uncertainties
• Systematic analysis of double Gamow-Teller sum rules
• Impact of microscopic structural transitions on particle stability and lifetimes of hot nuclei
• Study of entanglement in Ne, Mg, and Si isotopic chains
• New angular momentum coupling method based on Wigner rotation theory
• The calculation of single-nucleon energies of nuclei by considering two-body effective interaction, n(k,rho), and a Hartree-Fock inspired scheme
• Ab initio study of $\beta$-decay and pairing in $N=Z$ nuclei
• Seniority scenario for the 68-72Zn and 66-68Ni B(E2)^ difference
• Modification of tensor force in \textit{p}-shell effective interaction
• Correlation energy and quantum correlations in a solvable model
• libwignernj: a reusable C/C++/Fortran/Python library for exact Wigner symbols and related coefficients
• Ab initio no-core shell-model study of ${}^{20-23}$Na isotopes
• Investigation of Nuclear Structures of Ne Isotopes by Nuclear Shell Model
• Modification of single-hole-like states by configuration mixing in the ${}^{99-131}$In
• Boson Models with Interactions of Arbitrary Order
• Fermion quartets on the square lattice
• Ab initio study in the island of inversion within the two-major-shell valence space
• Electric dipole strength in $sd$-shell nuclei from small-angle proton scattering