New investigation of the neutron-neutron and neutron-proton final-state interaction in then-dbreakup reaction

Abstract

The neutron-neutron final-state interaction (FSI) has been investigated in the ${}^{2}\mathrm{H}(n,np)n$ 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 $\ensuremath{-}16.3\ifmmode\pm\else\textpm\fi{}0.4\mathrm{fm}$ while the relative cross section, normalized in the region of neutron-proton quasifree scattering, gives $\ensuremath{-}16.1\ifmmode\pm\else\textpm\fi{}0.4\mathrm{fm}.$ The relative data obtained at 16.6 MeV yielded ${a}_{\mathrm{nn}}=\ensuremath{-}16.2\ifmmode\pm\else\textpm\fi{}0.3\mathrm{fm}.$ 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.