Measurement of the $^1$S$_0$ Neutron-Neutron Scattering Length in $nd$ Breakup Using a Coincidence Geometry at 19 MeV

Measurements of the $^1$S$_0$ neutron-neutron scattering length, $a_{nn}$, in neutron-deuteron ($nd$) breakup were made at Triangle Universities Nuclear Laboratory (TUNL) at an incident neutron energy of 19.0 MeV. A coincidence geometry was utilized so that the momenta of the two neutrons in the final-state-interaction pair were measured along with the energy of the proton. A second detector pair was used to measure the well-established neutron-proton scattering length, $a_{np}$, as a check of our techniques. 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 $a_{np}$ and $a_{nn}$. Experimental details and our preliminary results will be presented.