Comparison Procedure and the Neutron-Neutron Scattering Length

At present the only means for obtaining information about the neutron-neutron scattering length $a_{\mathrm{nn}}$ and effective range $r_0$ are studies of reactions with three or more particles in the final state. It was felt that the comparative analysis of the various reactions which exhibit a ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ nucleon-nucleon interaction in the final state would be a reliable procedure by which to extract $a_{\mathrm{nn}}$. Thus the nucleon-induced breakup reactions of deuterons and trions were analyzed using the Born approximation and $S$-state wave functions for the deuteron, the trion and the two nucleons having a low relative energy in the final state. We found the comparative analysis of the trion breakup processes unsuccessful in the energy range considered. The values for $a_{\mathrm{nn}}$ extracted in analyses of the reaction $\mathrm{D}(n, p)2n$ around 14 MeV cannot be reconciled with the theoretical predictions based on exact charge symmetry and using either a hard-core or a velocity-dependent potential. The present analysis indicates, however, that for incident energies larger than 30 MeV the distorting interference effects are removed and that the deuteron breakup processes become more promising for the determination of $a_{\mathrm{nn}}$.