Four-nucleon shell-model calculations in a Faddeev-like approach

Abstract

We use equations for Faddeev amplitudes to solve the shell-model problem for four nucleons in the model space that includes up to 14 hbar Omega harmonic-oscillator excitations above the unperturbed ground state. Two- and three-body effective interactions derived from the Reid93 and Argonne V8' nucleon-nucleon potentials are used in the calculations. Binding energies, excitations energies, point-nucleon radii and electromagnetic and strangeness charge form factors for 4He are studied. The structure of the Faddeev-like equations is discussed and a formula for matrix elements of the permutation operators in a harmonic-oscillator basis is given. The dependence on harmonic-oscillator excitations allowed in the model space and on the harmonic-oscillator frequency is investigated. It is demonstrated that the use of the three-body effective interactions improves the convergence of the results.

22 pages, 13 figures, REVTex

References in corpus (9)

• Quantum Monte Carlo calculations of nuclei with A \leq 7
• Large-basis shell-model calculations for p-shell nuclei
• Measurement of the Proton's Neutral Weak Magnetic Form Factor
• Benchmark Calculations for the Triton Binding Energy for Modern NN Forces and the pi-pi Exchange Three-Nucleon Force
• Shell-model calculations for the three-nucleon system
• Neutron-3H and Proton-3He Zero Energy Scattering
• Solutions of the Faddeev-Yakubovsky equations for the four nucleons scattering states
• Spurious states in the Faddeev formalism for few-body systems
• Scattering states in the four nucleons system

Cited by in corpus (34)

• The Shell Model as Unified View of Nuclear Structure
• Properties of ${}^{12}$C in the {\it ab initio} nuclear shell-model
• Recent developments in no-core shell-model calculations
• Benchmark Test Calculation of a Four-Nucleon Bound State
• Ab initio shell model with a genuine three-nucleon force for the p-shell nuclei
• A high-precision variational approach to three- and four-nucleon bound and zero-energy scattering states
• Few-nucleon systems in translationally invariant harmonic oscillator basis
• State Dependent Effective Interaction for the Hyperspherical Formalism
• Converged ab initio calculations of heavy nuclei
• Evidence for Symplectic Symmetry in Ab Initio No-Core Shell Model Results for Light Nuclei
• Calculation of the Alpha--Particle Ground State within the Hyperspherical Harmonic Basis
• Physical Significance of q Deformation and Many-Body Interactions in Nuclei
• Modern Ab Initio Approaches and Applications in Few-Nucleon Physics with A \ge 4
• Nuclear structure with accurate chiral perturbation theory nucleon-nucleon potential: Application to 6Li and 10B
• Coupled-cluster calculations for valence systems around O-16
• Total Photoabsorption Cross Sections of A=6 Nuclei with Complete Final State Interaction
• Low energy $n-\nuc{3}{H}$ scattering : a novel testground for nuclear interaction
• \texttt{NuHamil}: A numerical code to generate nuclear two- and three-body matrix elements from chiral effective field theory
• Inversion doublets of 3N+N cluster structure in excited states of ${}^4$He
• Calculation of the ${}^6$Li ground state within the hyperspherical harmonic basis
• Beyond the Shell Model: The Canonical Nuclear Many-Body Problem as an Effective Theory
• Ab initio calculation of Li7 photodisintegration
• Ab-initio no-core shell model study of ${}^{10-14}$B isotopes with realistic NN interactions
• Similarity Renormalization Group Evolution of Many-Body Forces in a One-Dimensional Model
• Ab initio no-core shell model description of ${}^{10-14}$C isotopes
• The Form of the Effective Interaction in Harmonic-Oscillator-Based Effective Theory
• Effective Interactions for the Three-Body Problem
• Spectroscopic properties of 4He within a multiphonon approach
• Ab-initio no-core shell model study of ${}^{18-24}$Ne isotopes
• Study of structure and radii for ${}^{20-31}$Na isotopes using microscopic interactions
• No-core shell model for 48-Ca, 48-Sc and 48-Ti
• Multi-body wave function of ground and low-lying excited states using unornamented deep neural networks
• Nuclear structure properties of Si and P isotopes with the microscopic effective interactions
• No-core shell model for A = 47 and A = 49