Neutron-deuteron breakup experiment at En = 13 MeV : Determination of the 1S0 neutron-neutron scattering length ann

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 ${a}_{\mathit{nn}}=\ensuremath{-}18.7\ifmmode\pm\else\textpm\fi{}0.7$ fm is in excellent agreement with ${a}_{\mathit{nn}}=\ensuremath{-}18.6\ifmmode\pm\else\textpm\fi{}0.4$ 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 ${a}_{\mathit{nn}}=\ensuremath{-}18.8\ifmmode\pm\else\textpm\fi{}0.5$ fm, in agreement with the result obtained from the absolute cross-section measurements. Our result deviates from the world average of ${a}_{\mathit{nn}}=\ensuremath{-}16.7\ifmmode\pm\else\textpm\fi{}0.5$ 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.