Shell Model in the Complex Energy Plane

Abstract

This work reviews foundations and applications of the complex-energy continuum shell model that provides a consistent many-body description of bound states, resonances, and scattering states. The model can be considered a quasi-stationary open quantum system extension of the standard configuration interaction approach for well-bound (closed) systems.

Topical Review, J. Phys. G, Nucl. Part. Phys, in press (2008)

References in corpus (59)

• The density-matrix renormalization group
• An accurate nucleon-nucleon potential with charge-independence breaking
• The high-precision, charge-dependent Bonn nucleon-nucleon potential (CD-Bonn)
• Mean-field description of ground-state properties of drip-line nuclei: Pairing and continuum effects
• Few-Nucleon Forces and Systems in Chiral Effective Field Theory
• Exceptional Points of Non-hermitian Operators
• Self-consistent Green's function method for nuclei and nuclear matter
• Model-independent low momentum nucleon interaction from phase shift equivalence
• Gamow Shell Model Description of Neutron-Rich Nuclei
• The Non-Abelian Density Matrix Renormalization Group Algorithm
• The role of the rigged Hilbert space in Quantum Mechanics
• Two-Particle Resonant States in a Many-Body Mean Field
• Shell Structure of Exotic Nuclei
• Gamow Shell Model Description of Weakly Bound Nuclei and Unbound Nuclear States
• Discrete and continuum spectra in the unified shell model approach
• Measurement of two-halo neutron transfer reaction p(${}^{11}$Li,${}^9$Li)t at 3$A$ MeV
• Continuum Shell Model
• Two-proton radioactivity
• Density Matrix Renormalization Group and Reaction-Diffusion Processes
• Fine Structure in the Decay of Deformed Proton Emitters: Non-adiabatic Approach
• Theoretical description of deformed proton emitters: nonadiabatic coupled-channel method
• Survey of ground state neutron Spectroscopic Factors from Li to Cr isotopes
• Study of the ${}^{7}Be(p,\gamma {)}^{8}B$ and ${}^{7}Li(n,\gamma {)}^{8}Li$ capture reactions using the shell model embedded in the continuum
• Complex coupled-cluster approach to an ab-initio description of open quantum systems
• Theory of the two-proton radioactivity in the continuum shell model
• Proton-Neutron Coupling in the Gamow Shell Model: the Lithium Chain
• Density matrix renormalization group approach for many-body open quantum systems
• Gamow shell model and realistic nucleon-nucleon interactions
• A Pedestrian Introduction to Gamow Vectors
• Modified two-potential approach to tunneling problems
• Threshold Effects in Multi-channel Coupling and Spectroscopic Factors in Exotic Nuclei
• Gamow and R-matrix Approach to Proton Emitting Nuclei
• Analysis of the 16O(p,gamma)17F capture reaction using the shell model embedded in the continuum
• Recovery of the Schwarzschild Metric in Theories with Localized Gravity Beyond Linear Order
• Microscopic theory of the two-proton radioactivity
• The Density Matrix Renormalization Group for finite Fermi systems
• Shell model in the complex energy plane and two-particle resonances
• Resonances of 7He in the complex scaling method
• Shell corrections for finite depth potentials: Particle continuum effects
• Particle-unstable nuclei in the Hartree-Fock theory
• Jordan blocks and Gamow-Jordan eigenfunctions associated to a double pole of the S-matrix
• Three-body Coulomb breakup of 11Li in the complex scaling method
• Continuum Coupling and Single-Nucleon Overlap Integrals
• Shell Corrections for Finite-Depth Deformed Potentials: Green's Function Oscillator Expansion Method
• Study of Resonant Structures in a Deformed Mean-Field by the Contour Deformation Method in Momentum Space
• Effective Interaction Techniques for the Gamow Shell Model
• On the mean value of the energy for resonant states
• Antibound States and Halo Formation in the Gamow Shell Model
• Shell model description of 16O(p,gamma)17F and 16O(p,p)16O reactions
• Geometric Phases and Multiple Degeneracies in Harmonic Resonators
• First-forbidden mirror beta-decays in A=17 mass region
• Complex energy approaches for calculating isobaric analogue states
• The resonance amplitude associated with the Gamow states
• A study of nuclei of astrophysical interest in the continuum shell model
• Completeness of the Coulomb scattering wave functions
• Another Look at Just-So Solar Neutrino Oscillations
• Siegert pseudostate perturbation theory: one- and two-threshold cases
• Structure effects on the Coulomb dissociation of 8B at relativistic energies
• Description of resonances within the rigged Hilbert space

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• Recent developments in radioactive charged-particle emissions and related phenomena
• Super-Radiant Dynamics, Doorways, and Resonances in Nuclei and Other Open Mesoscopic Systems
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• Effects of symmetry breaking in finite quantum systems
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• Ab initio computation of the 17F proton-halo state and resonances in A = 17 nuclei
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• Nuclear Theory and Science of the Facility for Rare Isotope Beams
• Quantified Gamow Shell Model interaction for $psd$-shell nuclei
• Alpha Decay in the Complex Energy Shell Model
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• Recent Progress in Two-proton Radioactivity
• Probing the resonance of Dirac particle by the application of complex momentum representation
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• Isospin mixing and the continuum coupling in weakly bound nuclei
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• Ab initio no-core solutions for ${}^6$Li
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• First observation of unbound ${}^{11}$O, the mirror of the halo nucleus ${}^{11}$Li
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• Probing Nuclear forces beyond the drip-line using the mirror nuclei ${}^{16}$N and ${}^{16}$F
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• Unbound spectra of neutron-rich oxygen isotopes predicted by the Gamow shell model
• Spectroscopy of ${}^{26}$F to probe proton-neutron forces close to the drip line
• Challenges in Nuclear Structure Theory
• Energy Spectrum of Neutron-Rich Helium Isotopes: Complex Made Simple
• Single-particle and collective motion in unbound deformed ${}^{39}\text{Mg}$
• Gamow shell model description of ${}^4$He($d$,$d$) elastic scattering reactions
• Chiral three-nucleon force and continuum for dripline nuclei and beyond
• Toward Scalable Many-Body Calculations for Nuclear Open Quantum Systems using the Gamow Shell Model
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• Probing the Non-exponential Decay Regime in Open Quantum Systems
• A simple and efficient numerical scheme to integrate non-local potentials
• Neutron-rich calcium isotopes within realistic Gamow shell model calculations with continuum coupling
• Proton decays in ${}^{16}$Ne and ${}^{18}$Mg and isospin-symmetry breaking in carbon isotopes and isotones
• The rigged Hilbert space approach to the Gamow states
• Description of proton-rich nuclei in the $A\sim 20$ region with the Gamow shell model
• Gamow Shell Model description of Li isotopes and their mirror partners
• Exceptional points in the scattering continuum
• Nuclear three-body problem in the complex energy plane: Complex-Scaling-Slater method
• Precise comparison of the Gaussian expansion method and the Gamow shell model
• Numerical calculation of the decay widths, the decay constants, and the decay energy spectra of the resonances of the delta-shell potential
• Nucleon-nucleon correlations in the extreme oxygen isotopes
• Observation of the near-threshold intruder $0^{-}$ resonance in ${}^{12}$Be
• Spectroscopic factors in dripline nuclei
• Double-magicity of proton drip-line nucleus ${}^{22}$Si with \textit{ab initio} calculation
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• Search for excited states in ${}^{25}$O
• Closed-shell properties of ${}^{24}$O with {\em ab initio} coupled-cluster theory
• Calculation of the Thomas-Ehrman shift in ${}^{16}$F and ${}^{15}$O(p,p) cross section with the Gamow shell model
• Density matrix renormalization group description of the island of inversion isotopes ${}^{28-33}$F
• Bound states of dipolar molecules studied with the Berggren expansion method
• Using Continuum Level Density in the Pairing Hamiltonian: BCS and Exact Solutions
• Investigation of spectroscopic factors of deeply-bound nucleons in drip-line nuclei with the Gamow shell model
• Effective interactions and operators in no-core shell model
• Role of quadrupole deformation and continuum effects in the "island of inversion'' nuclei ${}^{28,29,31}$F
• Odd-even staggering in neutron drip line nuclei
• One-neutron halo structure of ${}^{29}$Ne
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• Structure of the neutron-rich N=7 isotones 10Li and 9He
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• Merging ab initio theory and few-body approach for $(d,p)$ reactions
• Weakly bound systems, continuum effects, and reactions
• Mirror Symmetry Breaking Disclosed in the Decay of Three-Proton Emitter 20Al
• Towards scalable bound-to-resonance extrapolations for few- and many-body systems
• Distributions of the $S$-matrix poles in Woods-Saxon and cut-off Woods-Saxon potentials
• Analysis of the unbound spectrum of ${}^{12}$Li
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• Trajectories of the S-matrix poles in Salamon-Vertse potential
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• Nucleon-nucleon resonances at intermediate energies using a complex energy formalism
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