Final-state interactions and neutron-neutron scattering parameters

A method is presented to extend the calculations of McVoy and Bander to determine the low-energy neutron-neutron scattering parameters from the spectrum of the reaction ${\pi }^{-}+d\to 2n+\gamma$. The transition amplitude for the capture reaction is derived in the impulse approximation and is related to 12 rotationally invariant amplitudes. The final-state interactions between the two neutrons are treated by means of dispersion relations and a closed-form exact solution is obtained in the effective range approximation and for different Bargmann parametrizations of the ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ neutron-neutron phase shift. A theoretical uncertainty of less than 0.3 fm is expected in the scattering length.