A high-precision variational approach to three- and four-nucleon bound and zero-energy scattering states

Abstract

The hyperspherical harmonic (HH) method has been widely applied in recent times to the study of the bound states, using the Rayleigh-Ritz variational principle, and of low-energy scattering processes, using the Kohn variational principle, of A=3 and 4 nuclear systems. When the wave function of the system is expanded over a sufficiently large set of HH basis functions, containing or not correlation factors, quite accurate results can be obtained for the observables of interest. In this paper, the main aspects of the method are discussed together with its application to the A=3 and 4 nuclear bound and zero-energy scattering states. Results for a variety of nucleon-nucleon (NN) and three-nucleon (3N) local or non-local interactions are reported. In particular, NN and 3N interactions derived in the framework of the chiral effective field theory and NN potentials from which the high momentum components have been removed, as recently presented in the literature, are considered for the first time within the context of the HH method. The purpose of this paper is two-fold. First, to present a complete description of the HH method for bound and scattering states, including also detailed formulas for the computation of the matrix elements of the NN and 3N interactions. Second, to report accurate results for bound and zero-energy scattering states obtained with the most commonly used interaction models. These results can be useful for comparison with those obtained by other techniques and are a significant test for different future approaches to such problems.

51 pages

References in corpus (62)

• An accurate nucleon-nucleon potential with charge-independence breaking
• The high-precision, charge-dependent Bonn nucleon-nucleon potential (CD-Bonn)
• Accurate Charge-Dependent Nucleon-Nucleon Potential at Fourth Order of Chiral Perturbation Theory
• Construction of high-quality Nucleon-Nucleon potential models
• Quantum Monte Carlo calculations of nuclei with A \leq 7
• Quantum Monte Carlo Calculations of $A\le 6$ Nuclei
• Realistic models of pion-exchange three-nucleon interactions
• The Two-Nucleon Potential from Chiral Lagrangians
• Few-Nucleon Forces and Systems in Chiral Effective Field Theory
• Properties of ${}^{12}$C in the {\it ab initio} nuclear shell-model
• Model-independent low momentum nucleon interaction from phase shift equivalence
• Quantum Monte Carlo calculations of A=8 nuclei
• Precise solution of few-body problems with stochastic variational method on correlated Gaussian basis
• Nuclear forces from chiral Lagrangians using the method of unitary transformation II: The two-nucleon system
• Peripheral Nucleon-Nucleon Phase Shifts and Chiral Symmetry
• Structure of A=10-13 nuclei with two- plus three-nucleon interactions from chiral effective field theory
• Quantum Monte Carlo calculations of $A=9,10$ nuclei
• Benchmark Test Calculation of a Four-Nucleon Bound State
• Nuclear forces from chiral Lagrangians using the method of unitary transformation I: Formalism
• Local three-nucleon interaction from chiral effective field theory
• Effective Field Theory of Nuclear Forces
• Reworking the Tucson-Melbourne Three-Nucleon Potential
• Low momentum nucleon-nucleon potential and shell model effective interactions
• Low momentum nucleon-nucleon potential and shell model effective interactions
• Momentum-space treatment of Coulomb interaction in three-nucleon reactions with two protons
• Modern nuclear force predictions for the alpha particle
• Precision Measurements of the Nucleon Strange Form Factors at Q^2 ~0.1 GeV^2
• Parameter-free effective field theory calculation for the solar proton-fusion and hep processes
• Chiral Symmetry and Three-Nucleon Forces
• Study of bound and scattering states in three-nucleon systems
• State Dependent Effective Interaction for the Hyperspherical Formalism
• Electromagnetic structure of A=2 and 3 nuclei and the nuclear current operator
• Low-momentum interaction in few-nucleon systems
• The alpha-particle based on modern nuclear forces
• Testing Non-local Nucleon-Nucleon Interactions in the Four-Nucleon Systems
• Four-nucleon scattering: Ab initio calculations in momentum space
• Polarization observables in p-d scattering below 30 MeV
• The three-nucleon bound state using realistic potential models
• Calculation of the Alpha--Particle Ground State within the Hyperspherical Harmonic Basis
• Towards a Model-Independent Low Momentum Nucleon-Nucleon Interaction
• Parity-Violating Electron Scattering and Neucleon Structure
• Low-momentum interactions with smooth cutoffs
• Precision neutron interferometric measurements and updated evaluations of the n-p and n-d coherent neutron scattering lengths
• Weak proton capture on 3He
• New calculation schemes for proton-deuteron scattering including the Coulomb interaction
• Nuclear structure with accurate chiral perturbation theory nucleon-nucleon potential: Application to 6Li and 10B
• Proton radii of 4,6,8He isotopes from high-precision nucleon-nucleon interactions
• The complex Kohn variational method applied to N-d scattering
• Observation of the Charge Symmetry Breaking d + d -> 4He + pi0 Reaction Near Threshold
• Four-nucleon shell-model calculations in a Faddeev-like approach
• Photo- and Electro-Disintegration of 3He at Threshold and pd Radiative Capture
• Variational Calculation on A=3 and 4 Nuclei with Non-Local Potentials
• Realistic Calculation of the hep Astrophysical Factor
• Neutron-3H and Proton-3He Zero Energy Scattering
• N-d scattering including electromagnetic forces
• Survey of charge symmetry breaking operators for dd -> alpha pi0
• Benchmark calculations for polarization observables in 3N scattering
• Ground State Wave Functions in the Hyperspherical Formalism for Nuclei with A > 4
• Modern nuclear force predictions for the neutron-deuteron scattering lengths
• proton-deuteron elastic scattering above the deuteron breakup
• Phase Shifts and Mixing Parameters for Elastic Proton-Deuteron Scattering
• Low-momentum interactions for nuclei

Cited by in corpus (142)

• Recent developments in no-core shell-model calculations
• Hyperon-nucleon interaction at next-to-leading order in chiral effective field theory
• Three-Nucleon Low-Energy Constants from the Consistency of Interactions and Currents in Chiral Effective Field Theory
• Ab initio coupled-cluster approach to nuclear structure with modern nucleon-nucleon interactions
• Minimally non-local nucleon-nucleon potentials with chiral two-pion exchange including $\Delta$'s
• Ab initio many-body calculations of nucleon-nucleus scattering
• Neutrino physics with the PTOLEMY project: active neutrino properties and the light sterile case
• Local chiral potentials and the structure of light nuclei
• Light-nuclei spectra from chiral dynamics
• The primordial deuterium abundance of the most metal-poor damped Lyman-alpha system
• Three-Nucleon Forces: Implementation and Applications to Atomic Nuclei and Dense Matter
• Frequency metrology in quantum degenerate helium: Direct measurement of the 2 3S1 - 2 1S0 transition
• Quantum Monte Carlo calculations of electromagnetic moments and transitions in A <= 9 nuclei with meson-exchange currents derived from chiral effective field theory
• The nuclear matter equation of state with consistent two- and three-body perturbative chiral interactions
• Symmetry-guided large-scale shell-model theory
• Frontiers in Nuclear Astrophysics
• Convergence properties of {\itshape ab initio} calculations of light nuclei in a harmonic oscillator basis
• Quantum Monte Carlo calculations of spectroscopic overlaps in $A\le 7$ nuclei
• Chiral effective field theory predictions for muon capture on deuteron and 3He
• Electromagnetic structure of A=2 and 3 nuclei in chiral effective field theory
• Evolving Nuclear Many-Body Forces with the Similarity Renormalization Group
• Frequency metrology of helium around 1083 nm and determination of the nuclear charge radius
• Ab initio many-body calculations of nucleon scattering on 4He, 7Li, 7Be, 12C and 16O
• Electromagnetic two-body currents of one- and two-pion range
• Implication of the proton-deuteron radiative capture for Big Bang Nucleosynthesis
• Modern Ab Initio Approaches and Applications in Few-Nucleon Physics with A \ge 4
• Ab initio many-body calculations of deuteron-4He scattering and 6Li states
• Effect of three-nucleon interaction in p-3He elastic scattering
• Local nucleon-nucleon and three-nucleon interactions within chiral effective field theory
• Impact of chiral hyperonic three-body forces on neutron stars
• On a redundancy in the parity-violating 2-nucleon contact Lagrangian
• Living on the edge of stability, the limits of the nuclear landscape
• Electromagnetic Structure of Few-Nucleon Ground States
• Bound state techniques to solve the multiparticle scattering problem
• Tritium $\beta$-decay in chiral effective field theory
• Benchmark calculation of n-3H and p-3He scattering
• Nuclear Currents in Chiral Effective Field Theory
• The isoscalar monopole resonance of the alpha particle: a prism to nuclear Hamiltonians
• Thermal neutron captures on $d$ and ${}^3$He
• Neutron-${}^3$H scattering above the four-nucleon breakup threshold
• N-d Elastic Scattering Using the Hyperspherical Harmonics Approach with Realistic Local and Non-Local Interactions
• Structure and decays of nuclear three-body systems: the Gamow coupled-channel method in Jacobi coordinates
• The Theory of Parity Violation in Few-Nucleon Systems
• Nuclear polarization corrections in the mu-4He+ Lamb shift
• Calculation of the ${}^6$Li ground state within the hyperspherical harmonic basis
• Comparative study of three-nucleon force models in $A=3,4$ systems
• Calculation of proton-${}^3$He elastic scattering between 7 and 35 MeV
• Local chiral interactions and magnetic structure of few-nucleon systems
• Muon capture on deuteron and 3He
• Efimov Physics and Connections to Nuclear Physics
• Short-range three-nucleon interaction from A=3 data and its hierarchical structure
• Parity- and time-reversal-violating nuclear forces
• Description of Four- and Five-Nucleon Systems by Solving Faddeev-Yakubovsky Equations in Configuration Space
• Non-resonant Density of States Enhancement at Low Energies for Three or Four Neutrons
• Power counting in chiral effective field theory and nuclear binding
• A chiral effective field theory study of hadronic parity violation in few-nucleon systems
• Fast emulation of quantum three-body scattering
• Integral relations for three-body continuum states with the adiabatic expansion
• The X17 boson and the ${}^3$H$(p,e^{+}{e}^{-}{)}^4$He and ${}^3$He$(n,e^{+}{e}^{-}{)}^4$He processes: a theoretical analysis
• Quantum electrodynamic calculation of the hyperfine structure of 3He
• Two- and three-nucleon contact interactions and ground-state energies of light- and medium-mass nuclei
• Nuclear structure corrections to the Lamb shift in ${\mu }^3$He${}^{+}$ and ${\mu }^3$H
• The Triton Charge Radius to Next-to-next-to-leading order in Pionless Effective Field Theory
• Three-cluster dynamics within an ab initio framework
• Benchmark calculation of p-3H and n-3He scattering
• Nuclei with up to $\mathbf{A}=6$ nucleons with artificial neural network wave functions
• Calculation of multichannel reactions in the four-nucleon system above breakup threshold
• Resonances of $A=4$ $T=1$ isospin triplet states within the \textit{ab initio} no-core Gamow shell model
• The parity-violating asymmetry in the 3He(n,p)3H reaction
• Gamow shell model description of ${}^4$He($d$,$d$) elastic scattering reactions
• Towards the understanding of the genuine three-body interaction for p$-$p$-$p and p$-$p$-\Lambda$
• Neutron spin rotation in \vec{n}-d scattering
• The harmonic hyperspherical basis for identical particles without permutational symmetry
• Calculation of neutron-${}^3$He scattering up to 30 MeV
• Momentum distributions and short-range correlations in the deuteron and ${}^3$He with modern chiral potentials
• Comparing proton momentum distributions in $A=2$ and 3 nuclei via ${}^2$H ${}^3$H and ${}^3$He $(e,e^{\prime }p)$ measurements
• Coherent deeply virtual Compton scattering off ${}^4$He
• Four-body calculation of ${}^2\mathrm{H}(d,p){}^3\mathrm{H}$ and ${}^2\mathrm{H}(d,n){}^3\mathrm{He}$ reactions above breakup threshold
• Efimov physics with $1/2$ spin-isospin fermions
• Charge and Magnetic Properties of Three-Nucleon Systems in Pionless Effective Field Theory
• Search for three-nucleon force effects on the longitudinal response function of 4He
• Break-up channels in muon capture on 3He
• Zemach moments and radii of 2,3H and 3,4He
• Deuteron-deuteron scattering above four-nucleon breakup threshold
• Solar fusion III: New data and theory for hydrogen-burning stars
• Do we know how to count powers in pionless and pionful effective field theory?
• The Faddeev-Yakubovsky symphony
• General integral relations for the description of scattering states using the hyperspherical adiabatic basis
• Three-body breakup within the fully discretized Faddeev equations
• Description of light nuclei in pionless effective field theory using the stochastic variational method
• Effect of the N3LO three-nucleon contact interaction on p-d scattering observables
• Time Reversal Violation in Light Nuclei
• Coulomb Excitation of Deuteron in Peripheral Collisions with a Heavy Ion
• Nonsymmetrized hyperspherical harmonics with realistic NN potentials
• The $p\Lambda$ and $pp\Lambda$ correlation functions
• Proton-${}^3$H scattering calculation: Elastic and charge-exchange reactions up to 30 MeV
• Magnetic structure of few-nucleon systems at high momentum transfers in a $\chi$EFT approach
• JLab Measurement of the ${}^4$He Charge Form Factor at Large Momentum Transfers
• Catching a glimpse of the parton structure of the bound proton
• Tribaryon configurations and the inevitable three nucleon repulsions at short distance
• Muon Capture on Deuteron and 3He: A Personal Review
• Effect of three nucleon forces in p-3He scattering
• Spectroscopic properties of 4He within a multiphonon approach
• Theoretical description of three- and four-nucleon scattering states using bound-state-like wave functions
• Heavy-baryon chiral perturbation theory approach to thermal neutron capture on ${}^{3}He$
• Studies of the Three-Body Breakup in Deuteron-Deuteron Collisions near the Quasi-Free Limit at 160 MeV
• Exact restoration of Galilei invariance in density functional calculations with quantum Monte Carlo
• ${}^3$H production via neutron-neutron-deuteron recombination
• Radiative pion capture in 2H, 3He and 3H
• Measurement of double-polarization asymmetries in the quasi-elastic ${}^3\overrightarrow{\mathrm{He}}(\vec{\mathrm{e}},{\mathrm{e}}^{\prime }\mathrm{p})$ process
• Microscopic three-cluster study of light exotic nuclei
• JLab Measurements of the 3He Form Factors at Large Momentum Transfers
• Comparative study of ${}^6$He $\beta$-decay based on different similarity-renormalization-group evolved chiral interactions
• Incoherent deeply virtual Compton scattering off ${}^4$He
• Six-bodies calculations using the Hyperspherical Harmonics method
• Subleading contributions to $N$-boson systems inside the universal window
• Chiral Electroweak Currents in Nuclei
• Variational Approximations in a Path-Integral Description of Potential Scattering
• Muon capture on deuteron and the neutron-neutron scattering length
• Investigation of the Cross Section for dd Elastic Scattering and dd$\to$ n${}^3$He Reactions at 160 MeV
• Computing an orthonormal basis of symmetric or antisymmetric hyperspherical harmonics
• Partial Rate Matrix for Dark Matter Scattering
• Muon capture on light nuclei
• Selected Topics in Three- and Four-Nucleon Systems
• Nonsymmetrized Hyperspherical Harmonics approach to A=6 system
• Local two- and three-nucleon chiral interactions
• Resonances in ${}^{12}$C and ${}^{24}$Mg: what do we learn from a microscopic cluster theory?
• Generalized parton distributions of light nuclei
• The excited state of the $\alpha$-particle: a benchmark study
• Theoretical study of the ${}^4\mathrm{He}(\gamma ,\mathrm{p}{)}^3\mathrm{H}$ and ${}^4\mathrm{He}(\gamma ,\mathrm{n}{)}^3\mathrm{He}$ reactions
• Three-body Forces in Oscillator Bases Expansion
• Femtoscopic study of the proton-proton and proton-deuteron systems in heavy-ion collisions at the LHC
• A Many-Body Density Energy Functional
• Three-Nucleon Forces
• Mass-Energy Equivalence in Bound Three-Nucleon Systems
• Electromagnetic Processes in $\chi$EFT
• Active learning emulators for nuclear two-body scattering in momentum space
• Examination of the multiple-scattering expansion in the four-nucleon system
• Description of the proton-decaying 0${}_2^{+}$ resonance of the $\alpha$ particle
• Analysis of three-nucleon forces effects in the $A=3$ system
• Deuteron-${}^3\mathrm{He}$ scattering using nucleon-${}^3\mathrm{He}$ optical potentials fitted to four-body amplitudes
• Study of nucleonic matter with a consistent two- and three-body perturbative chiral interaction