Extract neutron-neutron interaction strength and spatial-temporal dynamics of neutron emission from two-particle correlation function

The neutron-neutron ($nn$) correlation function has been measured in 25 MeV/u $^{124}$Sn+$^{124}$Sn reactions. Using the Lednick\'y-Lyuboshitz approach, the $nn$ scattering length and effective range ($f_{0}^{nn}$, $d_{0}^{nn}$), as well as the reduced space-time size $R^{(0)}$ of the neutron emission source are simultaneously extracted as ($18.9^{+1.3}_{-1.2}$ fm, $1.9^{+1.3}_{-1.0}$ fm) and $4.12 \pm 0.12$ fm, respectively. The measured $nn$ scattering length is consistent with the results obtained in the low-energy scattering $^{2}{\rm H}(\pi^{-},\gamma)2n$, indicating heavy-ion collisions can serve as an effective approach for measuring $nn$ interactions and further investigating the charge symmetry breaking of nuclear force. The space-time size extracted from momentum-gated correlation functions exhibits clear dependence on the pair momentum, with $R^{(0)}=2.8 \pm 0.1 $ fm and $4.9 \pm 0.2$ fm being determined for the high and low momentum neutrons, respectively.