We report on results of a kinematically complete neutron-deuteron breakup experiment performed at Triangle Universities Nuclear Laboratory using an $E_n=13$ MeV incident neutron beam. The ${}^1{S}_0$ neutron-neutron scattering length $a_{\mathit{nn}}$ has been determined for four production angles of the neutron-neutron final-state interaction configuration. The absolute cross-section data were analyzed with rigorous three-nucleon calculations. Our average value of $a_{\mathit{nn}}=-18.7\pm 0.7$ fm is in excellent agreement with $a_{\mathit{nn}}=-18.6\pm 0.4$ fm obtained from capture experiments of negative pions on deuterons. We also performed a shape analysis of the final-state interaction cross-section enhancements by allowing the normalization of the data to float. From these relative data, we obtained an average value of $a_{\mathit{nn}}=-18.8\pm 0.5$ fm, in agreement with the result obtained from the absolute cross-section measurements. Our result deviates from the world average of $a_{\mathit{nn}}=-16.7\pm 0.5$ fm determined from previous kinematically complete neutron-deuteron breakup experiments, including the most recent one carried out at Bonn. However, this low value for $a_{\mathit{nn}}$ is at variance with theoretical expectation and other experimental information about the sign of charge-symmetry breaking of the nucleon-nucleon interaction. In agreement with theoretical predictions, no evidence was found of significant three-nucleon force effects on the neutron-neutron final-state interaction cross sections.

• Received 26 April 2005

DOI:https://doi.org/10.1103/PhysRevC.73.034001