Measurements of the $^1$S$_0$ Scattering Lengths in Neutron-Deuteron Breakup at 19 MeV in a Coincidence Geometry

Measurements of the $^1$S$_0$ neutron-neutron ($nn$) and neutron-proton ($np$) scattering lengths, $a_{nn}$ and $a_{np}$ respectively, using neutron-induced deuteron breakup were made at Triangle Universities Nuclear Laboratory (TUNL) at an incident neutron energy of 19.0 MeV. Six liquid scintillator detectors were configured in a coincidence geometry to measure the momenta of the two neutrons in two $nn$ and $np$ final-state-interaction (FSI) pairs while the energy of the proton was determined using a C$_{6}$D$_{12}$ active target. The scattering lengths were extracted from the experimental cross sections by comparison to rigorous three-nucleon calculations using the CD Bonn nucleon-nucleon potential for various values of $a_{nn}$ and $a_{np}$. In this talk results from the two $nn$ and $np$ FSI measurements and the analysis to obtain $a_{nn}$ will be presented.