Final-state interactions and neutron-neutron scattering parameters

Abstract

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 ${\ensuremath{\pi}}^{\ensuremath{-}}+d\ensuremath{\rightarrow}2n+\ensuremath{\gamma}$. 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.NUCLEAR REACTIONS ${\ensuremath{\pi}}^{\ensuremath{-}}+d\ensuremath{\rightarrow}2n+\ensuremath{\gamma}$, exact dispersive treatment of $^{1}S_{0}$ final-state interactions, deuteron wave function. Variation of phase shifts.