We construct a phenomenological three-nucleon force (3NF) model that gives a good description of polarization observables in elastic nucleon-deuteron (N-$d$) 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-d scattering at 3 MeV. Predictions of the model 3NF on N-d polarization observables at higher energies are examined, and effects of each component on the observables are investigated.
The reaction of the elastic electron-deuteron scattering at high momentum transfer is investigated within the Bethe-Salpeter approach. The relativistic covariant Graz II separable kernel of nucleon-nucleon interactions is used to analyze the deuteron structure functions, form factors and tensor of polarization components. The modern data for the electromagmetic nucleons structure from the double polarization experiments as well as some other models of the nucleon form factors are considered.
A high-precision test of the Glauber formula for the amplitude of nucleon-deuteron scattering is performed. Nucleon-nucleon amplitudes used in the calculations depend on the spins of interacting particles, phase shifts, and mixing parameters. These amplitudes were derived by using the Nijmegen potentials. The differential cross sections for nucleon-deuteron scattering were calculated for the projectile-nucleon energies of 65, 95, 135, 150, 190, and 250~MeV, and the results of these calculations were compared with experimental data.
Three-nucleon force effects in polarization transfers from the doubly spin-polarized initial neutron-deuteron state to the outgoing neutron in neutron-deuteron scattering
A new computational method for solving the nucleon-deuteron breakup scattering problem has been applied to study the elastic neutron- and proton-deuteron scattering on the basis of the configuration-space Faddeev-Noyes-Noble-Merkuriev equations. This method is based on the spline-decomposition in the angular variable and on a generalization of the Numerov method for the hyperradius. 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 …
A new computational method for solving the nucleon-deuteron breakup scattering problem has been applied to study the inelastic neutron-deuteron scattering on the basis of the configuration-space Faddeev equations. This method is based on the spline-decomposition in the angular variable and on a generalization of the Numerov method for the hyperradius. The Merkuriev-Gignoux-Laverne approach has been generalized for arbitrary nucleon-nucleon potentials and with an arbitrary number of partial waves. Neutron-deuteron observables at the incident nucleon energy 14.1 MeV have been calculated using th…
Within the framework of the study of radiative corrections to the polarization observed in elastic $ed$-scattering in leptonic variables have been calculated the Born values of vector AB^L, AB^T and tensor AB^LL, AB^TT, AB^LT asymmetries. The deuteron wave functions in coordinate representation for eight nucleon-nucleon potentials (Nijm1, Nijm2, Nijm93, Reid93, Argonne v18, OBEPC, MT and Paris) have been used for numerical calculations of vector AB^i(p,teta) and tensor AB^ij(p,teta) asymmetries. The angular-momentum dependence of values vector and tensor asymmetries have been also evaluated in…
We examine a description of available cross section data for symmetric space star (SST) configurations in the neutron-deuteron (nd) and proton-deuteron (pd) breakup reaction using numerically exact solutions of the three-nucleon (3N) Faddeev equation based on two- and three-nucleon (semi)phenomenological and chiral forces. The predicted SST cross sections are very stable with respect to the underlying dynamics for incoming nucleon laboratory energies below $\approx 25$ MeV. We discuss possible origins of the surprising discrepancies between theory and data found in low-energy nd and pd SST bre…
The results from an investigation of the incoherent single pion electroweak production on the deuteron in the $Δ$(1232) region are reported. The importance of including the nucleon-nucleon final state interactions in extracting the neutrino-nucleon cross sections from the data obtained from the experiments on the deuteron target is demonstrated.
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,…
We calculate the lifetime of the deuteron from dimension-six quark operators that violate baryon number by one unit. We construct an effective field theory for $|ΔB|=1$ interactions that give rise to nucleon and $ΔB=1$ deuteron decay in a systematic expansion. We show that up to and including next-to-leading order the deuteron decay rate is given by the sum of the decay rates of the free proton and neutron. The first nuclear correction is expected to contribute at the few-percent level and comes with an undetermined low-energy constant. We discuss its relation to earlier potential-model calcul…
A general analytical expression has been obtained in the diffraction approximation for the polarization of nucleons arising in the deuteron stripping reaction on nuclei at intermediate energies of the incident particles. A tabulated density distribution of the target nucleus and a realistic wave function of the deuteron with correct asymptotic limits at large internucleon distances were used in the calculations. The nucleon-nucleus phase shifts were calculated in the Glauber formalism using the double folding potential. The calculated angular dependencies for the vector analyzing power $A_{y}$…
We investigate the sensitivity of the non-exclusive nucleon induced deuteron breakup reaction to the three-nucleon interaction and distributions of three-nucleon force effects in inclusive spectra. To this end we solve the three-nucleon Faddeev equation at a number of incoming nucleon laboratory energies using the CD Bonn nucleon-nucleon interaction alone or combined with the 2π-exchange Tucson-Melbourne three-nucleon force. Based on these solutions energy spectra of an outgoing nucleon, at a specified detection angle as well as spectra integrated over that angle, are calculated. By integratin…
The two-body break up of the deuteron is studied at high $Q^2$ kinematics, with main motivation to probe the deuteron at small internucleon distances. Such studies are associated with the probing of high momentum component of the deuteron wave function. For this, two main theoretical issues have been addressed such as electromagnetic interaction of the virtual photon with the bound nucleon and the strong interaction of produced baryons in the final state of the break-up reaction. Within virtual nucleon approximation we developed a new prescription to account for the bound nucleon effects in el…
We solve three-nucleon Faddeev equations with nucleon-nucleon and three-nucleon forces derived consistently in the framework of chiral perturbation theory at next-to-next-to-next-to-leading order in the chiral expansion. In this first investigation we include only matrix elements of the three-nucleon force for partial waves with the total two-nucleon (three-nucleon) angular momenta up to 3 (5/2). Low-energy neutron-deuteron elastic scattering and deuteron breakup reaction are studied. Emphasis is put on Ay puzzle in elastic scattering and cross sections in symmetric-space-star and neutron-neut…
Theoretical uncertainties of various types are discussed for the nucleon-deuteron elastic scattering observables at the incoming nucleon laboratory energies up to 200 MeV. We are especially interested in the statistical errors arising from uncertainties of parameters of a nucleon-nucleon interaction. The obtained uncertainties of the differential cross section and numerous scattering observables are in general small, grow with the reaction energy and amount up to a few percent at 200 MeV. We compare these uncertainties with the other types of theoretical errors like truncation errors, numerica…
A general analytical expressions for the cross-section and the polarization of nucleons arising in the inclusive deuteron stripping reaction have been derived in the diffraction approximation. The nucleon-nucleus phases were calculated in the framework of Glauber formalism and making use of the double-folding potential. The tabulated distributions of the target nucleus density and the realistic deuteron wave function with correct asymptotic at large nucleon-nucleon distances were used. The calculated angular dependences for the cross-sections and the analyzing powers of the $(\vec{d},p)$ react…
Trinucleon Photo Reactions with $Δ$-Isobar Excitation: Radiative Nucleon-Deuteron Capture and Two-Body Photo Disintegration of the Three-Nucleon Bound State
We investigate the role of the nucleon recoil for antikaon-deuteron scattering using EFT. In particular, we show that the leading correction to the static term that appears at order $ξ^{1/2}$ (where $ξ=m_K/M_N$) cancels completely in the double scattering process. We calculate the higher order recoil corrections and study the pattern of convergence of the expansion method. We find that the recoil correction to the double scattering process is of order of 10-15% of the static contribution.
Use of deuteron-induced spallation reactions at intermediate energies has recently been proposed for transmutation of several long-lived fission products (LLFPs). In the design study of a transmutation system using a deuteron primary beam, accurate cross section data of deuteron-induced reactions on the LLFPs are indispensable. Reliable model predictions play an important role in completing the necessary cross section data since currently available experimental data are very limited. Under the circumstances, we have been developing a code system dedicated for deuteron-induced reactions, which …
The effect of the nucleon recoil for antikaon-deuteron scattering is investigated in the framework of effective field theory. In particular, we concentrate on the calculation of the nucleon recoil effect for the double-scattering process. It is shown that the leading correction to the static term that emerges at order xi^{1/2} with xi=M_K/m_N vanishes due to a complete cancellation of individually large contributions. The resulting recoil effect in this process is found to be of order of 10-15% as compared to the static term. We also briefly discuss the application of the method in the calcula…
Deuteron-deuteron elastic scattering and transfer reactions in the energy regime above four-nucleon breakup threshold are described by solving exact four-particle equations for transition operators. Several realistic nuclear interaction models are used, including the one with effective many-nucleon forces generated by the explicit $Δ$-isobar excitation; the Coulomb force between protons is taken into account as well. Differential cross sections, deuteron analyzing powers, outgoing nucleon polarization, and deuteron-to-neutron polarization transfer coefficients are calculated at 10 MeV deuteron…
Perturbative calculations of nucleon-deuteron elastic scattering in chiral effective field theory
College of Physics, Sichuan University（四川大学物理学院）；Institute of Applied Physics and Computational Mathematics（应用物理与计算数学研究所）；School of Physics, Beihang University（北京航空航天大学物理学院）
We investigate how strong a hypothetical 1S0 bound state of two neutrons would affect different observables in the neutron-deuteron reactions. To that aim we extend our momentum space scheme of solving three-nucleon Faddeev equations to incorporate in addition to the deuteron also the 1S0 dineutron bound state. We discuss effects induced by dineutron on the angular distribution of the neutron-deuteron elastic scattering and cross sections of the deuteron breakup. A comparison to the available data for neutron-deuteron total cross sections and elastic scattering angular distributions cannot dec…
We present a practical method to solve the proton-deuteron scattering problem at energies above the three-body breakup threshold, in which we treat three-body integral equations in coordinate space accommodating long-range proton-proton Coulomb interactions. The method is examined for phase shift parameters, and then applied to calculations of differential cross sections in elastic and breakup reactions, analyzing powers, etc. with a realistic nucleon-nucleon force and three-nucleon forces. Effects of the Coulomb force and the three-nucleon forces on these observables are discussed in comparin…
The contribution of a three-nucleon (3N) force, acting between the neutron and proton in the incoming deuteron with a target nucleon, to the deuteron-target potential in the entrance channel of the $A(d,p)B$ reaction has been calculated within the adiabatic distorted wave approximation (ADWA). Four different 3N interaction sets from local chiral effective field theory ($χ$EFT) at next-to-next-to-leading order (N2LO) were used. Strong sensitivity of the adiabatic deuteron-target potential to the choice of the 3N force format has been found, which originates from the enhanced sensitivity to the …
The continuum-discretized coupled-channels method (CDCC) for exclusive reactions and the eikonal reaction theory (ERT) as an extension of CDCC to inclusive reactions are applied to deuteron induced reactions. The CDCC result reproduces experimental data on the reaction cross section for $d+^{58}$Ni scattering at 200 MeV/nucleon and ERT does data on the neutron-stripping cross section for inclusive $^7$Li$(d,n)$ reaction at 40 MeV. For deuteron induced reactions at 200 MeV/nucleon, target-dependence of the reaction, elastic-breakup, nucleon-stripping, nucleon-removal, complete- and incomplete-f…
