Neutron-deuteron breakup experiment at E{sub n}=13 MeV: Determination of the {sup 1}S{sub 0} neutron-neutron scattering length a{sub nn}

We report on results of a kinematically complete neutron-deuteron breakup experiment performed at Triangle Universities Nuclear Laboratory using an E{sub n}=13 MeV incident neutron beam. The {sup 1}S{sub 0} neutron-neutron scattering length a{sub 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{sub nn}=-18.7{+-}0.7 fm is in excellent agreement with a{sub nn}=-18.6{+-}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{sub nn}=-18.8{+-}0.5 fm, in agreement with the result obtained from the absolute cross-section measurements. Our result deviates from the world average of a{sub nn}=-16.7{+-}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{sub 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.