Neutron-neutron quasifree scattering in neutron-deuteron breakup at 10 MeV

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 $\pm 5.6\mathrm{\%}$. 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\mathrm{/}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.