Scattering into cones and flux across surfaces

The relation between the physical meaning of a nonrelativistic $N$-particle flux and its mathematical representation in quantum mechanics is discussed. We prove a theorem that equates the probability of finding an $N$-fragment system in the distant future in a given cone with the total probability that the fragments cross a distant surface subtended by the cone. Together with the scattering-into-cones theorem this result proves that the usually calculated number of fragments whose momenta in the distant future lie in a given cone is equal to the total counted number of fragments that, at any time, cross a subtended distant surface. It thus adds to both physically and mathematically cleaner underpinnings of scattering theory.