The neutron-neutron final-state interaction (FSI) has been investigated in the ${}^2\mathrm{H}\mathrm{}(n,np)n$ reaction at 25.3 and 16.6 MeV, detecting neutrons and protons in coincidence in a geometry which should enable a practically model-independent determination of the ${}^1{S}_0$ neutron-neutron scattering length $a_{\mathrm{nn}}.$ The analysis was performed by means of detailed Monte Carlo simulations based on rigorous three-body calculations with realistic nucleon-nucleon potentials. At 25.3 MeV, the value of $a_{\mathrm{nn}}$ deduced from the absolute cross section in the FSI peak is $-16.3\pm 0.4\mathrm{fm}$ while the relative cross section, normalized in the region of neutron-proton quasifree scattering, gives $-16.1\pm 0.4\mathrm{fm}.$ The relative data obtained at 16.6 MeV yielded $a_{\mathrm{nn}}=-16.2\pm 0.3\mathrm{fm}.$ In addition, the ${}^1{S}_0$ neutron-proton scattering length was measured at 25.2 MeV in the same configuration for comparison. While our results for $a_{\mathrm{nn}}$ are incompatible with those of a similar investigation performed recently at 13 MeV where the two neutrons were detected, both results for $a_{\mathrm{np}}$ are in good agreement with the accurately known value from free n-p scattering.

• Received 14 August 2000

DOI:https://doi.org/10.1103/PhysRevC.63.014003