Neutron-Neutron Scattering Length

The final-state interaction of the two neutrons from the reaction ${\pi }^{-}+d\to 2n+\gamma$ has a pronounced and distinctive effect on the momentum spectrum of the outgoing particles. In particular, the neutron spectrum is sharply peaked in the neighborhood of 2 Mev, with a shape that is quite sensitive to the strength of the $\mathrm{nn}$ interaction. In the region of this peak, the relative neutron-neutron momentum is so small that the $\mathrm{nn}$ interaction is completely characterized by its scattering length. Hence it is proposed that a measurement of the shape of the neutron spectrum from this reaction may provide a convenient means of measuring the neutron-neutron scattering length. Neutron spectra are calculated in an impulse approximation, for several assumed values of the scattering length. It appears from their shapes that, in this way, present neutron-detection techniques should be capable of determining the scattering length to within 25%.