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 Lednický-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 ($18.9_{-1.2}^{+1.3}$ fm, $1.9_{-1.0}^{+1.3}$ 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 ${}^2\mathrm{H}({\pi }^{-},\gamma )2n$, 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.