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.
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