New Measurement of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mrow><mml:msup><mml:mrow/><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msup></mml:mrow><mml:mi mathvariant="italic">S</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>Neutron-Neutron Scattering Length Using the Neutron-Proton Scattering Length as a Standard

This paper reports high-accuracy cross-section data taken for identical kinematic conditions of the neutron-proton $(\mathrm{np})$ and neutron-neutron $(\mathrm{nn})$ 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 ${a}_{\mathrm{nn}}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{-}18.7\ifmmode\pm\else\textpm\fi{}0.6\mathrm{fm}$ and ${a}_{\mathrm{np}}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{-}23.5\ifmmode\pm\else\textpm\fi{}0.8\mathrm{fm}$. The value obtained for ${a}_{\mathrm{nn}}$ in the present work is in agreement with that from ${\ensuremath{\pi}}^{\ensuremath{-}}d$ measurements but disagrees with values obtained from earlier neutron-deuteron breakup studies.