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We report the most precise determination of the $^{1}S_{0}$ neutron-neutron effective range parameter ($r_{nn}$) from neutron-neutron quasifree scattering in neutron-deuteron breakup. The experiment setup utilized a collimated beam of 15.5 MeV neutrons and an array of eight neutron detectors positioned at angles sensitive to several quasifree scattering kinematic configurations. The two neutrons emitted from the breakup reaction were detected in coincidence and time-of-flight techniques were used to determine their energies. The beam-target luminosity was measured in-situ with the yields from neutron-deuteron elastic scattering. Rigorous Faddeev-type calculations using the CD Bonn nucleon-nucleon potential were fit to our cross-section data to determine the value of $r_{nn}$. The analysis was repeated using a semilocal momentum-space regularized N$^4$LO$^+$ chiral interaction potential. We obtained values of $r_{nn} = 2.86 \pm 0.01 \,(stat) \pm 0.10 \,(sys)$ fm and $r_{nn} = 2.87 \pm 0.01 \,(stat) \pm 0.10 \,(sys)$ fm using the CD Bonn and N$^4$LO$^+$ potentials, respectively. Our results are consistent with charge symmetry and previously reported values of $r_{nn}$., Comment: Ver 1: 6 pages, 3 figures, 3 tables; Submitted to Phys Lett B; Ver 2: 8 pages, 3 figures, 3 tables; Changes: 1. Figure 2 plots neutron energy instead of time-of-flight and shows kinematic locus for clarity. Plot true coincidence spectra instead of raw and accidental coincidence spectra. 2. Figure 3 vertical instead of horizontal. 3. Minor text changes for clarity

New measurements of the neutron-neutron quasifree scattering cross section in neutron-deuteron breakup at an incident neutron energy of 10.0 MeV are reported. The experiment setup was optimized to evaluate the technique for determining the integrated beam-target luminosity in neutron-neutron coincidence cross-section measurements in neutron-deuteron breakup. The measurements were carried out with a systematic uncertainty of $\pm 5.6 \%$. Our data are in agreement with theoretical calculations performed using the CD-Bonn nucleon-nucleon potential in the Faddeev formalism. The measured integrated cross section over the quasifree peak is $20.5 \pm 0.5 \text{(stat)} \pm 1.1 \text{(sys)}$ mb/sr$^2$ in comparison with the theory prediction of 20.1 mb/sr$^{2}$. These results validate our technique for determining the beam-target luminosity in neutron-deuteron breakup measurements., Comment: 23 pages, 12 figures, published in Physical Review C