Gamow Shell Model Description of Weakly Bound Nuclei and Unbound Nuclear States

Abstract

We present the study of weakly bound, neutron-rich nuclei using the nuclear shell model employing the complex Berggren ensemble representing the bound single-particle states, unbound Gamow states, and the non-resonant continuum. In the proposed Gamow Shell Model, the Hamiltonian consists of a one-body finite depth (Woods-Saxon) potential and a residual two-body interaction. We discuss the basic ingredients of the Gamow Shell Model. The formalism is illustrated by calculations involving {\it several} valence neutrons outside the double-magic core: ${}^{6-10}$He and ${}^{18-22}$O.

19 pages, 20 encapsulated PostScript figures

References in corpus (10)

• Gamow Shell Model Description of Neutron-Rich Nuclei
• Two-Particle Resonant States in a Many-Body Mean Field
• 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
• Theoretical Aspects of Science with Radioactive Nuclear Beams
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• Shell corrections for finite depth potentials: Particle continuum effects
• On the mean value of the energy for resonant states
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Cited by in corpus (91)

• The Shell Model as Unified View of Nuclear Structure
• Radioactive decays at limits of nuclear stability
• Shell Model in the Complex Energy Plane
• Ab initio coupled-cluster approach to nuclear structure with modern nucleon-nucleon interactions
• Shell Structure of Exotic Nuclei
• Recent development of complex scaling method for many-body resonances and continua in light nuclei
• Discrete and continuum spectra in the unified shell model approach
• Continuum Shell Model
• Super-Radiant Dynamics, Doorways, and Resonances in Nuclei and Other Open Mesoscopic Systems
• Ab-initio No-Core Gamow Shell Model calculations with realistic interactions
• 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
• From bound states to the continuum
• Threshold Effects in Multi-channel Coupling and Spectroscopic Factors in Exotic Nuclei
• Gamow and R-matrix Approach to Proton Emitting Nuclei
• Quantified Gamow Shell Model interaction for $psd$-shell nuclei
• Charge radii and neutron correlations in helium halo nuclei
• Ab-initio computation of neutron-rich oxygen isotopes
• Alpha Decay in the Complex Energy Shell Model
• Living on the edge of stability, the limits of the nuclear landscape
• Isospin mixing and the continuum coupling in weakly bound nuclei
• Ab initio no-core solutions for ${}^6$Li
• Toward understanding the microscopic origin of nuclear clustering
• Two-proton emission and related phenomena
• Dineutron structure in ${}^8$He
• Structure and decays of nuclear three-body systems: the Gamow coupled-channel method in Jacobi coordinates
• Open problems in theory of nuclear open quantum systems
• Gamow shell model description of proton scattering on ${}^{18}$Ne
• Description of the proton and neutron radiative capture reactions in the Gamow shell model
• Bound, virtual and resonance $S$-matrix poles from the Schrödinger equation
• Nuclear Halos and Drip Lines in Symmetry-Conserving Continuum HFB Theory
• Effective Field Theory and the Gamow Shell Model: The 6He Halo Nucleus
• Density matrix renormalization group approach to two-fluid open many-fermion systems
• An above-barrier narrow resonance in ${}^{15}$F
• Continuum Coupling and Single-Nucleon Overlap Integrals
• Gamow-Hartree-Fock-Bogoliubov Method: Representation of quasiparticles with Berggren sets of wave functions
• Gamow shell-model calculations of drip-line oxygen isotopes
• Gamow shell model description of radiative capture reactions ${}^6$Li$(p,\gamma )$${}^7$Be and ${}^6$Li$(n,\gamma )$${}^7$Li
• Effective Interaction Techniques for the Gamow Shell Model
• Study of Resonant Structures in a Deformed Mean-Field by the Contour Deformation Method in Momentum Space
• Generalized contour deformation method in momentum space: two-body spectral structures and scattering amplitudes
• Asymptotic normalization coefficients and continuum coupling in mirror nuclei
• Single-particle and collective motion in unbound deformed ${}^{39}\text{Mg}$
• Antibound States and Halo Formation in the Gamow Shell Model
• Gamow shell model description of ${}^4$He($d$,$d$) elastic scattering reactions
• Chiral three-nucleon force and continuum for dripline nuclei and beyond
• Tunneling Theory for Tunable Open Quantum Systems of Ultracold Atoms in One-Dimensional Traps
• Proton decays in ${}^{16}$Ne and ${}^{18}$Mg and isospin-symmetry breaking in carbon isotopes and isotones
• A simple and efficient numerical scheme to integrate non-local potentials
• Neutron-rich calcium isotopes within realistic Gamow shell model calculations with continuum coupling
• The rigged Hilbert space approach to the Gamow states
• Structure of positive energy states in a deformed mean-field potential
• Gamow Shell Model description of Li isotopes and their mirror partners
• Description of proton-rich nuclei in the $A\sim 20$ region with the Gamow shell model
• Continuum and three-nucleon force in Borromean system: The 17Ne case
• Eigenvector continuation for emulating and extrapolating two-body resonances
• Precise comparison of the Gaussian expansion method and the Gamow shell model
• Electric multipole response of the halo nucleus ${}^6$He
• Continuum and Symmetry-Conserving Effects in Drip-line Nuclei Using Finite-range Forces
• Description of the 17F(p,gamma)18Ne radiative capture reaction in the continuum shell model
• Numerical treatment of long-range Coulomb potential with Berggren bases
• Spectroscopy of 9C via resonance scattering of protons on 8B
• Calculation of the Thomas-Ehrman shift in ${}^{16}$F and ${}^{15}$O(p,p) cross section with the Gamow shell model
• Nuclear Structure Calculations with Coupled Cluster Methods from Quantum Chemistry
• Complex energy approaches for calculating isobaric analogue states
• The resonance amplitude associated with the Gamow states
• Bound states of dipolar molecules studied with the Berggren expansion method
• Effective interactions and operators in no-core shell model
• Gamow Shell-Model Description of Weakly Bound and Unbound Nuclear States
• From nucleons to nuclei to fusion reactions
• Spectroscopic factors of resonance states with the Gamow shell model
• The strength of beta-decays to the continuum
• Weakly bound systems, continuum effects, and reactions
• Gamow shell model description of the radiative capture reaction ${}^8$Li$(n,\gamma )$${}^9$Li
• Resonant spectra of quadrupolar anions
• Bound and resonance states of the dipolar anion of hydrogen cyanide: competition between threshold effects and rotation in an open quantum system
• Nuclear structure far from stability
• On the solution of a pairing problem in the continuum
• The Analytic Continuation of the Lippmann-Schwinger Eigenfunctions, and Antiunitary Symmetries
• Gamow shell model calculations for the Thomas-Ehrman shift in new isotopes 21Al
• Gamow shell model predictions for six-proton unbound nucleus ${}^{20}$Si
• ${}^{19}$F$(p,\gamma )$${}^{20}$Ne reaction rate and the puzzling calcium abundance in metal poor stars
• Non-Hermitian Quantum Mechanics Approach for Extracting and Emulating Continuum Physics Based on Bound-State-Like Calculations
• New method for extracting quasi-bound states from the continuum
• Gamow shell model study of the 17Ne(p, p) reaction and of isospin symmetry breaking in 18Na
• Self-consistent Green's function calculation of 16O at small missing energies
• Description of ${}^7$Be and ${}^7$Li within the Gamow Shell Model
• Strongly interacting few-fermion systems in a trap
• Green's Function Formalism for Impurity-Induced Resonances in Sub-barrier Proton-Nucleus Scattering