Concepts of multiparticle time delay

Abstract

This paper studies two concepts of time delay in few-particle scattering. The first is a global time delay that refers to the total advancement or retardation of the entire wave-packet motion owing to the presence of interactions not contained in the asymptotic Hamiltonian. The second type, the angular time delay, is the early or late arrival of a particle in a counter subtending an angle $\theta$ with respect to the incident beam direction. In the two-body problem the magnitude of this time delay is known to be $\left(\frac{d}{dE}\right)f(E,\theta )$, where $f(E,\theta )$ is the scattering amplitude at energy $E$. We discuss the definition of these two kinds of time delay in the three-body problem. We provide a generalization of the relation between angular time delay and the scattering amplitude that is valid for elastic, rearrangement, and breakup scattering. The interdependence of these two kinds of multichannel time delay is established. Possible physical applications of the resulting theory are discussed.