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

Triton calculations with π\pi and ρ\rho exchange three-nucleon forces

The Faddeev equations are solved in momentum space for the trinucleon bound state with the new Tucson-Melbourne $\pi$ and $\rho$ exchange three-nucleon potentials. The three-nucleon potentials are combined with a variety of realistic two-nucleon potentials. The dependence of the triton binding energy on the $\pi NN$ cut-off parameter in the three-nucleon potentials is studied and found to be reduced compared to the case with pure $\pi$ exchange. The $\rho$ exchange parts of the three-nucleon potential yield an overall repulsive effect. When the recommended parameters are employed, the calculated triton binding energy turns out to be very close to its experimental value. Expectation values of various components of the three-nucleon potential are given to illustrate their significance for binding.Comment: 17 pages Revtex 3.0, 4 figures. Accepted for publication in Phys. Rev.

Potential reuse of coal mine wastewater: a case study in Quang Ninh, Vietnam

In Vietnam, the local regulation and environmental impact are driving coal mining industry to reuse the large volume of wastewater it produces. The co-research project between National University of Civil Engineering (NUCE) and Mitsubishi Rayon Corporation (MRC) has started early 2013 to evaluate if the MRC membranes could be a great tool for treatment of coal mine wastewater for reuse. The experiment were conducted at one of coal mine plants in Quang Ninh province, Vietnam. It was found that pre-treatment of coal mine wastewater was an important part in the treatment process. The MRC membrane was a significant barrier to maintain stable and high quality effluent to meet the requirement of Vietnam national technical standard for domestic use

Analyzing power in nucleon-deuteron scattering and three-nucleon forces

Three-nucleon forces have been considered to be one possibility to resolve the well known discrepancy between experimental values and theoretical calculations of the nucleon analyzing power in low energy nucleon-deuteron scattering. In this paper, we investigate possible effects of two-pion exchange three-nucleon forces on the analyzing power and the differential cross section. We found that the reason for different effects on the analyzing power by different three-nucleon forces found in previous calculations is related to the existence of the contact term. Effects of some variations of two-pion exchange three-nucleon forces are investigated. Also, an expression for the measure of the nucleon analyzing power with quartet P-wave phase shifts is presented.Comment: 11 pages including 2 eps figures, use epsfig.sty, to appear in Phys. Rev.

Momentum and Coordinate Space Three-nucleon Potentials

In this paper we give explicit formulae in momentum and coordinate space for the three-nucleon potentials due to $\rho$ and $\pi$ meson exchange, derived from off-mass-shell meson-nucleon scattering amplitudes which are constrained by the symmetries of QCD and by the experimental data. Those potentials have already been applied to nuclear matter calculations. Here we display additional terms which appear to be the most important for nuclear structure. The potentials are decomposed in a way that separates the contributions of different physical mechanisms involved in the meson-nucleon amplitudes. The same type of decomposition is presented for the $\pi - \pi$ TM force: the $\Delta$, the chiral symmetry breaking and the nucleon pair terms are isolated.Comment: LATEX, 33 pages, 3 figures (available as postscript files upon request

Adjoint of the Global Eulerian Lagrangian Coupled Atmospheric transport model (A-GELCA v1.0): development and validation

Abstract. We present the development of the Adjoint of the Global Eulerian–Lagrangian Coupled Atmospheric (A-GELCA) model that consists of the National Institute for Environmental Studies (NIES) model as an Eulerian three-dimensional transport model (TM), and FLEXPART (FLEXible PARTicle dispersion model) as the Lagrangian plume diffusion model (LPDM). The tangent and adjoint components of the Eulerian model were constructed directly from the original NIES TM code using an automatic differentiation tool known as TAF (Transformation of Algorithms in Fortran; http://www.FastOpt.com), with additional manual pre- and post-processing aimed at improving the performance of the computing, including MPI (Message Passing Interface). As results, the adjoint of Eulerian model is discrete. Construction of the adjoint of the Lagrangian component did not require any code modification, as LPDMs are able to track a significant number of particles back in time and thereby calculate the sensitivity of observations to the neighboring emissions areas. Eulerian and Lagrangian adjoint components were coupled at the time boundary in the global domain.The results are verified using a series of test experiments. The forward simulation shown the coupled model is effective in reproducing the seasonal cycle and short-term variability of CO2 even in the case of multiple limiting factors, such as high uncertainty of fluxes and the low resolution of the Eulerian model. The adjoint model demonstrates the high accuracy compared to direct forward sensitivity calculations and fast performance. The developed adjoint of the coupled model combines the flux conservation and stability of an Eulerian discrete adjoint formulation with the flexibility, accuracy, and high resolution of a Lagrangian backward trajectory formulation. </jats:p

Covariant equations for the three-body bound state

The covariant spectator (or Gross) equations for the bound state of three identical spin 1/2 particles, in which two of the three interacting particles are always on shell, are developed and reduced to a form suitable for numerical solution. The equations are first written in operator form and compared to the Bethe-Salpeter equation, then expanded into plane wave momentum states, and finally expanded into partial waves using the three-body helicity formalism first introduced by Wick. In order to solve the equations, the two-body scattering amplitudes must be boosted from the overall three-body rest frame to their individual two-body rest frames, and all effects which arise from these boosts, including the Wigner rotations and rho-spin decomposition of the off-shell particle, are treated exactly. In their final form, the equations reduce to a coupled set of Faddeev-like double integral equations with additional channels arising from the negative rho-spin states of the off-shell particle.Comment: 57 pages, RevTeX, 6 figures, uses epsf.st

Neutron-3H and Proton-3He Zero Energy Scattering

The Kohn variational principle and the (correlated) Hyperspherical Harmonics technique are applied to study the n-3H and p-3He scattering at zero energy. Predictions for the singlet and triplet scattering lengths are obtained for non-relativistic nuclear Hamiltonians including two- and three-body potentials. The calculated n-3H total cross section agrees well with the measured value, while some small discrepancy is found for the coherent scattering length. For the p-3He channel, the calculated scattering lengths are in reasonable agreement with the values extrapolated from the measurements made above 1 MeV.Comment: 13 pages, REVTEX, 1 figur