Few-nucleon Systems Research Articles

An Algebraic Model of Nucleon Systems with Rules of Isospin Superselection

A simple algebraic model with rules of isospin superselection is formulated and tested on few-nucleon systems. It is shown that physically obtainable states corresponding to the bound states of these nucleons can be gained by applying symmetrical monoidal C* categories whose objects are G-modules, and whose morphisms are G-invariant homomorphisms.

Study of various few-body systems using Gaussian expansion method (GEM)

We review our calculation method, Gaussian expansion method (GEM), and its applications to various few-body (3- to 5-body) systems such as 1) few-nucleon systems, 2) few-body structure of hypernuclei, 3) clustering structure of light nuclei and unstable nuclei, 4) exotic atoms/molecules, 5) cold atoms, 6) nuclear astrophysics and 7) structure of exotic hadrons. Showing examples in our published papers, we explain i) high accuracy of GEM calculations and its reason, ii) wide applicability of GEM and iii) successful predictions by GEM calculations before measurements. GEM was proposed 30 years ago and has been applied to a variety of subjects. To solve few-body Schroedinger equations accurately, use is made of the Rayleigh-Ritz variational method for bound states, the complex-scaling method for resonant states and the Kohn-type variational principle to S-matrix for scattering states. The total wave function is expanded in terms of few-body Gaussian basis functions spanned over all the sets of rearrangement Jacobi coordinates. Gaussians with ranges in geometric progression work very well both for short-range and long-range behavior of the few-body wave functions. Use of Gaussians with complex ranges gives much more accurate solution when the wave function has many oscillations.

Correlations imposed by the unitary limit between few-nucleon systems, nuclear matter, and neutron stars.

The large values of the singlet and triplet two-nucleon scattering lengths locate the nuclear system close to the unitary limit. This particular position strongly constrains the low-energy observables in the three-nucleon system as depending on one parameter, the triton binding energy, and introduces correlations in the low-energy sector of light nuclei. Here we analyze the propagation of these correlations to infinite nuclear matter showing that its saturation properties, the equation of state of β-stable nuclear matter, and several properties of neutron stars, as their maximum mass, are well determined solely by a few number of low-energy quantities of the two- and three-nucleon systems. In this way we make a direct link between the universal behavior observed in the low-energy region of few-nucleon systems and fundamental properties of nuclear matter and neutron stars.

Few-nucleon and many-nucleon systems with semilocal coordinate-space regularized chiral nucleon-nucleon forces

We employ a variety of ab initio methods including Faddeev-Yakubovsky equations, No-Core Configuration Interaction Approach, Coupled-Cluster Theory and In-Medium Similarity Renormalization Group to perform a comprehensive analysis of the nucleon-deuteron elastic and breakup reactions and selected properties of light and medium-mass nuclei up to 48Ca using the recently constructed semilocal coordinate-space regularized chiral nucleon-nucleon potentials. We compare the results with those based on selected phenomenological and chiral EFT two-nucleon potentials, discuss the convergence pattern of the chiral expansion and estimate the achievable theoretical accuracy at various chiral orders using the novel approach to quantify truncation errors of the chiral expansion without relying on cutoff variation. We also address the robustness of this method and explore alternative ways to estimate the theoretical uncertainty from the truncation of the chiral expansion.

Three-nucleon force contribution in the distorted-wave theory of (d,p) reactions

The distorted-wave theory of A ( d , p ) B reactions, widely used to analyze experimental data, is based on a Hamiltonian that includes only two-nucleon interactions. However, numerous studies of few-nucleon systems and many modern developments in nuclear structure theory show the importance of the three-nucleon ( 3 N ) force. The purpose of this paper is to study the contribution of the 3 N force of the simplest possible form to the A ( d , p ) B reaction amplitude. This contribution is given by a new term that accounts for the interaction of the neutron and proton in the incoming deuteron with one of the target nucleons. This term involves a new type of nuclear matrix elements containing an infinite number of target excitations in addition to the main part associated with the traditional overlap function between A and B . The nuclear matrix elements are calculated for double-closed shell targets within a mean field theory where target excitations are shown to be equivalent to exchanges between valence and core nucleons. These matrix elements can be readily incorporated into available reaction codes if the 3 N interaction has a spin-independent zero-range form. Distorted-wave calculations are presented for a contact 3 N force with the volume integral fixed by the chiral effective field theory at the next-to-next-to-leading order. For this particular choice, the 3 N contribution is noticeable, especially at high deuteron incident energies. No 3 N effects are seen for incident energies below the Coulomb barrier. The finite range can significantly affect the 3 N contribution to the ( d , p ) cross sections. Finite-range studies require new formal developments and, therefore, their contribution is preliminarily assessed within the plane-wave Born approximation, together with sensitivity to the choice of the deuteron model.

Structure of the Lightest Tin Isotopes.

We link the structure of nuclei around ^{100}Sn, the heaviest doubly magic nucleus with equal neutron and proton numbers (N=Z=50), to nucleon-nucleon (NN) and three-nucleon (NNN) forces constrained by data of few-nucleon systems. Our results indicate that ^{100}Sn is doubly magic, and we predict its quadrupole collectivity. We present precise computations of ^{101}Sn based on three-particle-two-hole excitations of ^{100}Sn, and we find that one interaction accurately reproduces the small splitting between the lowest J^{π}=7/2^{+} and 5/2^{+} states.

Large-scale exact diagonalizations reveal low-momentum scales of nuclei

Ab initio methods aim to solve the nuclear many-body problem with controlled approximations. Virtually exact numerical solutions for realistic interactions can only be obtained for certain special cases such as few-nucleon systems. Here we extend the reach of exact diagonalization methods to handle model spaces with dimension exceeding $10^{10}$ on a single compute node. This allows us to perform no-core shell model (NCSM) calculations for 6Li in model spaces up to $N_\mathrm{max} = 22$ and to reveal the 4He+d halo structure of this nucleus. Still, the use of a finite harmonic-oscillator basis implies truncations in both infrared (IR) and ultraviolet (UV) length scales. These truncations impose finite-size corrections on observables computed in this basis. We perform IR extrapolations of energies and radii computed in the NCSM and with the coupled-cluster method at several fixed UV cutoffs. It is shown that this strategy enables information gain also from data that is not fully UV converged. IR extrapolations improve the accuracy of relevant bound-state observables for a range of UV cutoffs, thus making them profitable tools. We relate the momentum scale that governs the exponential IR convergence to the threshold energy for the first open decay channel. Using large-scale NCSM calculations we numerically verify this small-momentum scale of finite nuclei.

Recent progress in ab-initio studies of nuclear reactions of astrophysical interest with A ≤ 3

We review the most recent theoretical studies of nuclear reactions of astrophysical interest involving few-nucleon systems. In particular, we focus on the consequences for the solar neutrino fluxes of the recent determination for the astrophysical S-factor of the proton weak capture by proton, and on the radiative capture of protons by deuterons in the energy range of interest for Big Bang Nucleosynthesis.

Onset of η nuclear binding

Recent studies of η nuclear quasibound states by the Jerusalem-Prague Collaboration are reviewed, focusing on stochastic variational method self consistent calculations of η few-nucleon systems. These calculations suggest that a minimum value Re aηN ≈ 1 fm (0.7 fm) is needed to bind η3He (η4He).

Experimental Studies of Few-nucleon Systems. Dynamics of the $3N$ Interaction in Cross Sections

Experimental Studies of Few-nucleon Systems. Dynamics of the $3N$ Interaction in Cross Sections

Proton-Proton Fusion and Tritium β Decay from Lattice Quantum Chromodynamics.

The nuclear matrix element determining the pp→de^{+}ν fusion cross section and the Gamow-Teller matrix element contributing to tritium β decay are calculated with lattice quantum chromodynamics for the first time. Using a new implementation of the background field method, these quantities are calculated at the SU(3) flavor-symmetric value of the quark masses, corresponding to a pion mass of m_{π}∼806 MeV. TheGamow-Teller matrix element in tritium is found to be 0.979(03)(10) at these quark masses, which is within 2σ of the experimental value. Assuming that the short-distance correlated two-nucleon contributions to the matrix element (meson-exchange currents) depend only mildly on the quark masses, as seen for the analogous magnetic interactions, the calculated pp→de^{+}ν transition matrix element leads to a fusion cross section at the physical quark masses that is consistent with its currently accepted value. Moreover, the leading two-nucleon axial counterterm of pionless effective field theory is determined to be L_{1,A}=3.9(0.2)(1.0)(0.4)(0.9) fm^{3} at a renormalization scale set by the physical pion mass, also agreeing within the accepted phenomenological range. This work concretely demonstrates that weak transition amplitudes in few-nucleon systems can be studied directly from the fundamental quark and gluon degrees of freedom and opens the way for subsequent investigations of many important quantities in nuclear physics.

The theory of hadronic parity violation

Parity-violating interactions between nucleons are the manifestation of an interplay of strong and weak interactions between quarks in the nucleons. Compared to the dominant parity-conserving part, the parity-violating component of the nuclear force is typically suppressed by approximately 6 to 7 orders of magnitude or more. Due to the short range of the weak interactions, however, it provides a unique probe of the strong dynamics that confine quarks into nucleons. An ongoing experimental program is mapping out this weak component of the nuclear force in few-nucleon systems. I will discuss recent theoretical progress based on effective field theory methods to analyze and interpret hadronic parity violation in few-nucleon systems, with a particular focus on two- and three-nucleon systems.

Time-Dependent Correlated Gaussian Approach to the Nuclear Response of Few-Nucleon Systems

Nuclear responses involve the information on nuclear dynamics as well as underlying interactions. To describe them theoretically, one faces the difficulty in treating many-body continuum states. A newly developed time-dependent correlated Gaussian basis allows us to describe the response function without explicit construction of the many-body continuum states. As simple examples, the photoabsorption reactions of \(^2\)H and \(^3\)He are presented. In both cases, the calculations are remarkably improved compared to those with time-independent correlated Gaussian.

Recent Progresses in Ab-Initio Studies of Low-Energy Few-Nucleon Reactions of Astrophysical Interest

We review the most recent theoretical studies of nuclear reactions of astrophysical interest involving few-nucleon systems. In particular, we focus on the radiative capture of protons by deuterons in the energy range of interest for Big Bang Nucleosynthesis. Related to this, we will discuss also the most recent calculation of tritium $$\beta $$ -decay. Two frameworks will be considered, the conventional and the chiral effective field theory approach.

Invariant Coordinates in Breakup Reactions

Systematic experimental studies of few-nucleon systems expose various dynamical ingredients which play an important role in correct description of observables, such as three-nucleon force, Coulomb force and relativistic effects. A large set of existing experimental data for ^1H(d, p p)n reaction allows for systematic investigations of these dynamical effects, which vary with energy and appear with different strength in certain observables and phase space regions. Moreover, systematic comparisons with exact theoretical calculations, done in variables related to the system dynamics in a possibly direct ways is a very important tool to verify and improve the existing description of the nucleon interaction. Examples of experimental data for a breakup reaction, transformed to the variables based on Lorentz-invariants are compared with modern theoretical calculations.

Parity- and Time-Reversal-Invariance-Violating Nucleon-Nucleon Interactions in the Large-$$N_c$$ Expansion

Violations of parity (P) and time reversal invariance (T) in few-nucleon systems provide interesting tests of our understanding of the Standard Model as well as sensitive probes of Beyond-the-Standard-Model physics. Because of the small size of the symmetry-violating effects, experimental constraints on symmetry-violating nucleon-nucleon interactions are currently weak, if they exist at all. We analyze both P-violating T-conserving and P-violating T-violating nucleon-nucleon interactions in terms of the large-\(N_c\) expansion of QCD to provide additional theoretical constraints. This analysis leads to a hierarchy of terms in symmetry-violating potentials, establishes relations between couplings, and helps to delineate the terms that should be most important in phenomenological applications.

The CST: Its Achievements and Its Connection to the Light Cone

I review the applications of the Covariant Spectator Theory (CST) since its inception in 1969. Applications discussed here include calculations of NN scattering, 3N bound states, electromagnetic form factors of few-nucleon systems, and the recent successes in describing the dynamical generation of quark mass and the meson spectrum using a chirially invariant quark–antiquark interaction that includes confinement. The common origin of the Light Cone technique and the CST, which dates back to the 1970’s, will be discussed.

Experimental Study of Three-Nucleon Dynamics in the Dp Breakup Collisions Using the WASA Detector

Until recently, all calculations of breakup observables were carried out in a non-relativistic regime. The relativistic treatment of the breakup reaction in 3 N system is quite a new achievement. The detailed study of various aspects of few-nucleon system dynamics in medium energy region, with a particular emphasis on investigation of relativistic effects and their interplay with three nucleon force (3NF) becomes feasible with increasing available energy in the three nucleon system. Therefore an experiment to investigate the ^1H(d, pp)n breakup cross section using a deuteron beam of 300, 340, 380 and 400 MeV and the WASA detector has been performed at COSY-Jülich. The almost 4pi geometry of the WASA detector gives an unique possibility to study variety of kinematic configurations, which reveal different sensitivity to aspects of dynamics of the three nucleon system. The main steps of the analysis, including energy calibration, PID, normalization and efficiency studies, and their impact on the final accuracy of the result, are discussed.

Chiral dynamics with (non)strange quarks

We review the results and achievements of the project B.3 . Topics addressed include pion photoproduction off the proton and off deuterium, three-flavor chiral perturbation theory studies, chiral symmetry tests in Goldstone boson decays, the development of unitarized chiral perturbation theory to next-to-leading order, the two-pole structure of the Λ(1405), the dynamical generation of the lowest S 11 resonances, the theory of hadronic atoms and its application to various systems, precision studies in light-meson decays based on dispersion theory, the Roy–Steiner analysis of pion–nucleon scattering, a high-precision extraction of the elusive pion–nucleon σ -term, and aspects of chiral dynamics in few-nucleon systems.

Two-nucleon scattering in a modified Weinberg approach with a symmetry-preserving regularization

We consider the nucleon-nucleon scattering problem by applying time-ordered perturbation theory to the Lorentz invariant formulation of baryon chiral perturbation theory. Using a symmetry preserving higher derivative form of the effective Lagrangian, we exploit the freedom of the choice of the renormalization condition and obtain an integral equation for the scattering amplitude with an improved ultraviolet behavior. The resulting formulation is used to quantify finite regulator artifacts in two-nucleon phase shifts as well as in the chiral extrapolations of the S-wave scattering lengths and the deuteron binding energy. This approach can be straightforwardly extended to analyze few-nucleon systems and processes involving external electroweak sources.