Improved Convergence in the Three-Nucleon System at Very Low Energies

Abstract

Neutron-deuteron scattering in the context of ``pion-less'' Effective Field Theory at very low energies is investigated to next-to-next-to-leading order. Convergence is improved by fitting the two-nucleon contact interactions to the tail of the deuteron wave-function, a procedure known as Z-parameterisation and extended here to the three-nucleon system. The improvement is particularly striking in the doublet-S wave (triton) channel, where better agreement to potential-model calculations and better convergence from order to order in the power counting is achieved for momenta as high as \sim 120 MeV. Investigating the cut-off dependence of the phase-shifts, one confirms numerically the analytical finding that the first momentum-dependent three-body force enters at N2LO. The other partial waves converge also substantially faster. Effective-range parameters of the nd-system are determined, e.g. for the quartet-S-wave scattering length a_q=[6.35\pm0.02] fm, which compares favourably both in magnitude and uncertainty with recent high-precision potential-model determinations. Differential cross-sections up to E_{lab}\approx 15 MeV agree with data.

38 pages LaTeX2e with 11 figures, using graphicx (33 .eps files included). Petty changes. Version to be published by Nucl. Phys. A

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• The three-body problem with short-range forces: renormalized equations and regulator-independent results
• The spin-dependent nd scattering length - a proposed high-accuracy measurement

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