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-$d$) 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.Comment: 12 pages, 6 figures, submitted to Phys. Rev.

Low Energy Proton-Deuteron Scattering with a Coulomb-Modified Faddeev Equation

A modified version of the Faddeev three-body equation to accommodate the Coulomb interaction, which was used in the study of three-nucleon bound states, is applied to the proton-deuteron scattering problem at energies below the three-body breakup threshold. A formal derivation of the equation in a time-independent scattering theory is given. Numerical results for phase shift parameters are presented to be compared with those of another methods and results of the phase shift analysis. Differential cross sections and nucleon analyzing powers are calculated with the effects of three-nucleon forces, and these results are compared with recent experimental data. The difference between the nucleon analyzing power in proton-deuteron scattering and that in neutron-deuteron scattering is discussed.Comment: 23 pages, 6 eps figures, use FBSart.cls and FBSmath.cl

Coordinate space proton-deuteron scattering calculations including Coulomb force effects

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 comparing with experimental data.Comment: 15 pages, 14 figures, submitted to PR

η\eta photoproduction off the deuteron and low-energy η\eta-nucleon interaction

We study $\eta$ photoproduction off the deuteron ($\gamma d\to\eta pn$) at a special kinematics: $\sim 0.94$ GeV of the photon beam energy and $\sim 0^\circ$ of the scattering angle of the proton. This kinematics is ideal to extract the low-energy $\eta$-nucleon scattering parameters such as $a_{\eta N}$ (scattering length) and $r_{\eta N}$ (effective range) because the $\eta$-nucleon elastic scattering is significantly enhanced. We show that if a ratio $R$, the $\gamma d\to\eta pn$ cross section divided by the $\gamma p\to\eta p$ cross section convoluted with the proton momentum distribution in the deuteron, is measured with 5% error, ${\rm Re}[a_{\eta N}]$ (${\rm Re}[r_{\eta N}]$) can be determined at the precision of $\sim\pm$0.1 fm ($\sim\pm$0.5 fm), significantly narrowing down the currently estimated range of the parameters. The measurement is ongoing at the Research Center for Electron Photon Science (ELPH), Tohoku University.Comment: 4 pages, 5 figures, Contribution to the Proceedings for 8th International Conference on Quarks and Nuclear Physics (QNP2018), November 13-17, 2018, Tsukuba, Japa

Operation of Faddeev-Kernel in Configuration Space

We present a practical method to solve Faddeev three-body equations at energies above three-body breakup threshold as integral equations in coordinate space. This is an extension of previously used method for bound states and scattering states below three-body breakup threshold energy. We show that breakup components in three-body reactions produce long-range effects on Faddeev integral kernels in coordinate space, and propose numerical procedures to treat these effects. Using these techniques, we solve Faddeev equations for neutron-deuteron scattering to compare with benchmark solutions.Comment: 20 pages, 8 figures, to be published in Few-Body System

Central and tensor components of three-nucleon forces in low-energy proton-deuteron scattering

Contributions of three-nucleon forces (3NF) to proton-deuteron scattering observables at energies below the deuteron breakup threshold are studied by solving the Faddeev equation that includes the Coulomb interaction. At E_p=3.0 MeV, we find that the central part of a two-pion exchange 3NF removes the discrepancy between measured cross sections and the calculated ones by two-nucleon forces, and improves the agreement with T_{22} experimental data. However, the tensor part of the 3NF fails in reproducing data of the analyzing power T_{21} by giving worse agreement between the measured and the calculated. Detailed examinations of scattering amplitudes suggest that a P-wave contribution in spin quartet tensor amplitudes has unsuitable sign for reproducing the T_{21} data.Comment: 6 pages, 6 figure

How to construct a coordinate representation of a Hamiltonian operator on a torus

The dynamical system of a point particle constrained on a torus is quantized \`a la Dirac with two kinds of coordinate systems respectively; the Cartesian and toric coordinate systems. In the Cartesian coordinate system, it is difficult to express momentum operators in coordinate representation owing to the complication in structure of the commutation relations between canonical variables. In the toric coordinate system, the commutation relations have a simple form and their solutions in coordinate representation are easily obtained with, furthermore, two quantum Hamiltonians turning up. A problem comes out when the coordinate system is transformed, after quantization, from the Cartesian to the toric coordinate system.Comment: 17 pages, LaTeX, 1 Figure included as a compressed uuencoded postscript fil