Elastic Nucleon-deuteron Research Articles

Significance of chiral three-nucleon force contact terms for understanding of elastic nucleon-deuteron scattering

We investigate the importance of the three-nucleon (3N) force contact terms in elastic nucleon-deuteron (Nd) scattering by applying the N$^4$LO$^+$ chiral semi-local momentum space (SMS) regularized nucleon-nucleon (NN) chiral potential supplemented by N$^2$LO and all subleading N$^4$LO three-nucleon force (3NF) contact terms. Strength parameters of the contact terms were obtained by least squares fitting of theoretical predictions to cross section and analyzing powers data at three energies of the impinging nucleon. Although the N$^3$LO contributions to the 3N force were completely neglected, the results calculated with the contact terms multiplied by the fitted strength parameters yield an improved description of the elastic Nd scattering observables in a wide range of incoming nucleon energies below the pion production threshold.

Two-Pion Exchange Three-Nucleon Force Effects in Elastic Nucleon–Deuteron Scattering Cross Sections

Differential cross sections for elastic nucleon–deuteron scattering at intermediate energies are calculated by solving the Faddeev equation in coordinate space using interaction models consisting of a two-nucleon potential and three-nucleon potentials based on the exchange of two pions among three nucleons. Attractive effects of the pion-exchange at medium range region in the three-nucleon potential are taken into account by using a larger cutoff mass parameter and by adding phenomenological repulsive three-nucleon potentials as a counterpart. It is shown that these effects increase the cross sections at backward angles, which tends to reduce discrepancies between theoretical calculations and experimental data.

Nucleon-deuteron scattering with the JISP16 potential

The nucleon-nucleon J-matrix Inverse Scattering Potential JISP16 is applied to elastic nucleon-deuteron (Nd) scattering and the deuteron breakup process at the lab. nucleon energies up to 135 MeV. The formalism of the Faddeev equations is used to obtain 3N scattering states. We compare predictions based on the JISP16 force with data and with results based on various NN interactions: the CD Bonn, the AV18, the chiral force with the semi-local regularization at the 5th order of the chiral expansion and with low-momentum interactions obtained from the CD Bonn force as well as with the predictions from the combination of the AV18 NN interaction and the Urbana IX 3N force. JISP16 provides a satisfactory description of some observables at low energies but strong deviations from data as well as from standard and chiral potential predictions with increasing energy. However, there are also polarization observables at low energies for which the JISP16 predictions differ from those based on the other forces by a factor of two. The reason for such a behavior can be traced back to the P-wave components of the JISP16 force. At higher energies the deviations can be enhanced by an interference with higher partial waves and by the properties of the JISP16 deuteron wave function. In addition, we compare the energy and angular dependence of predictions based on the JISP16 force with the results of the low-momentum forces obtained with different values of the momentum cutoff parameter. We found that such low-momentum forces can be employed to interpret the Nd elastic scattering data only below some specific energy which depends on the cutoff parameter. Since JISP16 is defined in a finite oscillator basis, it has properties similar to low momentum interactions and its application to the description of Nd scattering data is limited to a low momentum transfer region.

Studies of three-nucleon systems with improved chiral forces

Recently developed chiral two-nucleon (2N) potentials are applied to various processes in three-nucleon (3N) systems within the approach based on Faddeev equations. The predictions for the cross sections in elastic nucleon-deuteron (Nd) scattering and for radiative proton-deuteron (pd) capture are similar to results based on the AV18 potential. The very good convergence with respect to the chiral expansion and a weak dependence on a regularization parameter are observed. This gives hope that the Hamiltonian combining these 2N potentials with consistent 3N forces will become an important tool to study nuclear structure and processes.

Elastic nucleon-deuteron scattering and breakup with chiral forces

Results on three-nucleon (3N) elastic scattering and breakup below the pion production threshold are discussed. The large discrepancies found between a theory based on numerical solutions of 3N Faddeev equations with standard nucleon-nucleon (NN) potentials only and data point to the need for three-nucleon forces (3NF’s). This notion is supported by the fact that another possible reason for the discrepancies in elastic nucleon-deuteron (Nd) scattering, relativistic effects, turned out to be small. Results for a new generation of chiral NN forces (up to N 4 LO) together with theoretical truncation errors are shown. They support conclusions obtained with standard NN potentials

Configuration-Space Faddeev Calculation for Proton–Deuteron Elastic Scattering Observables

A new computational method for solving the nucleon–deuteron breakup scattering problem has been applied to study the elastic nucleon–deuteron scattering on the basis of the configuration-space Faddeev–Noyes–Noble–Merkuriev equations. The Merkuriev–Gignoux–Laverne approach has been generalized for arbitrary nucleon–nucleon potentials and with an arbitrary number of partial waves. The nucleon–deuteron observables at the incident nucleon energy 3 MeV have been calculated using the charge-independent AV14 nucleon–nucleon potential including the Coulomb force for the proton–deuteron scattering. Results have been compared with those of other authors and with experimental proton–deuteron scattering data.

Relativistic Effects in Neutron–Deuteron Elastic Scattering and Breakup

We solved the Faddeev equation in a Poincaré invariant model of the three-nucleon system. Two-body interactions are generated so that when they are added to the two-nucleon invariant mass operator (rest energy) the two-nucleon S matrix is identical to the experimental S matrix modeled with a given nucleon–nucleon interaction. Cluster properties of the three-nucleon S-matrix determine how these two-nucleon interactions are embedded in the three-nucleon mass operator. Differences in the predictions of the relativistic and corresponding non-relativistic models for elastic and breakup processes are investigated. Of special interest are effects of relativity on the elastic scattering angular distribution and total cross sections, the lowering of the A y maximum in elastic nucleon-deuteron (Nd) scattering below ≈25 MeV caused by the Wigner spin rotations and the significant changes of the breakup cross sections in certain regions of the phase-space.

RELATIVISTIC EFFECTS IN 3N REACTIONS

We solved the three-nucleon Faddeev equation in a Poincaré invariant model of the three-nucleon system. Two-body interactions are generated so that when they are added to the two-nucleon invariant mass operator (rest energy) the two-nucleon S matrix is identical to the non-relativistic S matrix with a CD Bonn interaction. Cluster properties of the three-nucleon S -matrix determine how these two-nucleon interactions are embedded in the three-nucleon mass operator. Differences in the predictions of the relativistic and corresponding non-relativistic models for elastic and breakup processes are investigated. Of special interest are the lowering of the Ay maximum in elastic nucleon-deuteron (Nd) scattering below ≈ 25 MeV caused by the Wigner spin rotations and the significant changes of the breakup cross sections in certain regions of the phase-space.

Relativistic effects in the 3N continuum and the A y puzzle

The three-nucleon (3N) Faddeev equation is solved in a Poincare-invariant model of the three-nucleon system. Two-body interactions are generated so that when they are added to the two-nucleon invariant mass operator (rest energy) the two-nucleon S-matrix is identical to the non-relativistic S-matrix with a CD Bonn interaction. Cluster properties of the three-nucleon S-matrix determine how these two-nucleon interactions are embedded in the three-nucleon mass operator. Differences in the predictions of the relativistic and corresponding non-relativistic models for elastic and breakup processes are investigated. Of special interest are the lowering of the Ay maximum in elastic nucleon-deuteron (Nd) scattering below ≈25 MeV caused by the Wigner spin rotations and the significant changes of the breakup cross sections in certain regions of the phase space.

Spin-dependent three-nucleon force effects on nucleon-deuteron scattering

We construct a phenomenological three-nucleon force (3NF) model that gives a good description of polarization observables in elastic nucleon-deuteron ($N\text{\ensuremath{-}}d$) scattering at a low energy together with a realistic nucleon-nucleon force and a 3NF arising from the exchange of two pions. Parameters of the model, which consists of spin-independent, spin-orbit, and tensor components, are determined to reproduce the three-nucleon binding energy and polarization observables in $N\text{\ensuremath{-}}d$ scattering at 3 MeV. Predictions of the 3NF model on $N\text{\ensuremath{-}}d$ polarization observables at higher energies are examined, and the effects of each component on the observables are investigated.

ChiralNNmodel andAypuzzle

We analyze the results by chiral NN models for the two-nucleon system and calculate the predictions for the nucleon vector analyzing power of elastic nucleon-deuteron (Nd) scattering, Ay, by these models. Our conclusion is that a QUANTITATIVE chiral two-nucleon potential does not resolve the Nd Ay puzzle (when only two-body forces are included).

Potential independent structure on elastic nucleon–deuteron scattering

Potential independent structure on elastic nucleon–deuteron scattering

Nucleon-nucleon pion-exchange tested in three-body reactions.

Variants of a one-boson-exchange potential are applied to elastic nucleon-deuteron and electron-deuteron scattering. The models differ with respect to the treatment of the pion-nucleon vertex, where either a small coupling constant or a soft form factor is employed. We find that these variations do not affect [ital Nd] observables, but that they have a sizable effect on [ital ed] quantities via exchange currents of the pion. Taking into account also exchange currents of the [pi][prime] reduces the effect to a large extent.

Two-Nucleon Interactions, the Unitary Model, and Polarization in Elastic Nucleon-Deuteron Scattering

Two-Nucleon Interactions, the Unitary Model, and Polarization in Elastic Nucleon-Deuteron Scattering

Polarization in Elastic Nucleon-Deuteron Scattering

An approximate $K$-matrix calculation of elastic nucleon-deuteron scattering is carried out including the effects of two-nucleon tensor forces. The results of these computations, which are carried out in the energy range from 11 to 40 MeV, are in reasonable agreement with the experimental nucleon polarizations and differential cross sections.

Elastic Nucleon-Deuteron Scattering in a Soluble Model as a Test of the Impulse Approximation

A comparison of the results of the Born and impulse approximations for a well-defined situation is made by calculating the nucleon-deuteron differential elastic cross sections in both approximations at incident nucleon laboratory energies of 32, 94, and 146 Mev. In order to carry out the impulse approximation computation in complete detail, including, in particular, contributions from off- energy-shell two-particle matrix elements, the assumption is made that the two- particle scattering is completely described by effective range theory. This assumption, though incorrect, nevertheless retains some of the features of the actuai physical situation and provides a means of comparing the results of calculations using the impulse approximation and the Born approximation as well as a way of studying the effect of including two-particle matrix elements off the energy shell. Exact solutions to the two-particle model are written down with the aid of the Gel'fand-Levitan theory and are used in a precise numerical evaluation of the impulse approximation expressions. The results of the Born and impulse approximations differ considerably. Also, indications are that, as expected, the pickup term (which dominates at large angles) is not adequately treated by either of the above approximations. When this term is not considered, a study ofmore » the remaining expressions shows that off-energy-shell effects are significant for the deuteron wave functions employed. In view of the rather restrictive assumptions made on the twoparticle data, a detailed comparison of the results with experiment is not possible. Nevertheless, there is a suggestion that the impulse approximation, including offenergy-shell effects, describes the experimental results best. (auth)« less