In the modern description of nuclear forces based on chiral effective field theory, four-nucleon operators with unknown coupling constants appear. These couplings can be fixed by a fit to the low partial waves of neutron-proton scattering. We show that the so determined numerical values can be understood on the basis of phenomenological one-boson-exchange models. We also extract these values from various modern high accuracy nucleon-nucleon potentials and demonstrate their consistency and remarkable agreement with the values in the chiral effective field theory approach. This paves the way for estimating the low-energy constants of operators with more nucleon fields and/or external probes.
The Faddeev equation for three-body scattering at arbitrary energies is formulated in momentum space and directly solved in terms of momentum vectors without employing a partial wave decomposition. In its simplest form the Faddeev equation for identical bosons, which we are using, is a three-dimensional integral equation in five variables, magnitudes of relative momenta and angles. This equation is solved through Padé summation. Based on a Malfliet-Tjon-type potential, the numerical feasibility and stability of the algorithm for solving the Faddeev equation is demonstrated. Special attention is given to the selection of independent variables and the treatment of three-body break-up singularities with a spline based method. The elastic differential cross section, semi-exclusive d(N,N ′ ) cross sections and total cross sections of both elastic and breakup processes in the intermediate energy range up to about 1 GeV are calculated and the convergence of the multiple scattering series is investigated in every case. In general a truncation in the first or second order in the two-body t-matrix is quite insufficient.
The nucleon-nucleon ͑NN͒ t matrix is calculated directly as function of two vector momenta for different realistic NN potentials. To facilitate this a formalism is developed for solving the two-nucleon LippmannSchwinger equation in momentum space without employing a partial wave decomposition. The total spin is treated in a helicity representation. Two different realistic NN interactions, one defined in momentum space and one in coordinate space, are presented in a form suited for this formulation. The angular and momentum dependence of the full amplitude is studied and displayed. A partial wave decomposition of the full amplitude it carried out to compare the presented results with the well-known phase shifts provided by those interactions.PACS number͑s͒: 21.45.ϩv, 13.75.Cs
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