This paper reports high-accuracy cross-section data taken for identical kinematic conditions of the neutron-proton $\left(\mathrm{np}\right)$ and neutron-neutron $\left(\mathrm{nn}\right)$ final-state interactions in the ${}^2\mathrm{H}(n,nnp)$ reaction at an incident mean neutron energy of 13.0 MeV. These data were analyzed with rigorous three-nucleon calculations to determine the ${}^1{S}_0$ $\mathrm{np}$ and $\mathrm{nn}$ scattering lengths, $a_{\mathrm{np}}$ and $a_{\mathrm{nn}}$. Our results are $a_{\mathrm{nn}}=-18.7\mathrm{}\pm 0.6\mathrm{fm}$ and $a_{\mathrm{np}}=-23.5\mathrm{}\pm 0.8\mathrm{fm}$. The value obtained for $a_{\mathrm{nn}}$ in the present work is in agreement with that from ${\pi }^{-}d$ measurements but disagrees with values obtained from earlier neutron-deuteron breakup studies.

• Received 8 December 1998

DOI:https://doi.org/10.1103/PhysRevLett.83.3788