Improved convergence in the three-nucleon system at very low energies Original Research Article

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 View the MathML source. 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 View the MathML source, which compares favourably both in magnitude and uncertainty with recent high-precision potential-model determinations. Differential cross-sections up to View the MathML source agree with data.