Haag-Ruelle approximation of collision states

We investigate the rate of convergence of the Haag-Ruelle approximation Ψ(t) at large timest for arbitrary collision states Ψ with finite energy. An improved estimate of the norm distance ∥Ψ?Ψ(t)∥ is given. In particular for states Ψ with smooth asymptotic wave functions it turns out that ∥Ψ?Ψ(t)∥ approaches 0 almost liket ^?3/4.