Determination of the $^1S_0$ Neutron-Neutron Scattering Length Using nd Breakup in Recoil Geometry at 19 MeV

There is a significant discrepancy between the recent measurements of the $^1S_0$ neutron-neutron ({\it nn}) scattering length ($a_{nn}$). Gonz$\acute a$lez Trotter {\em et al.} [1] reported a value of $a_{nn} = -18.7 \pm 0.6$ fm from their nn coincidence cross-section measurements at a neutron beam energy of 13 MeV, while Huhn {\em et al.} [2] obtained $a_{nn} = -16.3 \pm 0.4$ fm from their nn final-state interaction (FSI) cross-section measurements made at 25 MeV using proton recoil geometry. We report the preliminary results of a new determination of $a_{nn}$ at 19 MeV at TUNL made using the neutron-deuteron breakup reaction in recoil proton geometry. The recoil proton and one of the outgoing neutrons were detected in coincidence and their energies were measured using time-of-flight techniques. Details of the experiment, analysis, and preliminary results will be presented. [1]$ D.E. Gonz$\acute{a}$lez Trotter {\it et al}., Phys. Rev. C~{\bf 73}, 034001 (2006). [2] V.H. Huhn {\it et al}., Phys. Rev. Lett.~{\bf 85}, 1190 (2000).