Time delay in atomic and molecular collisions and photoionisation/photodetachment

It is remarkable that time delay is an experimentally measurable quantity, but time itself is not. Time delay in quantum collisions and in photoionisation/photodetachment of atomic and molecular systems is reviewed in this paper. Wigner–Eisenbud formalism of time delay in quantum collision of a wavepacket with a target is discussed. Its equivalence with Smith's formalism of time delay, based on an independent basis for time delay in terms of excess particle density in the collision zone, is demonstrated. Similarity and difference between quantum collision of an electron with a positive atomic/molecular ion and photoionisation/photodetachment of a neutral atom/molecule are discussed, and the underlying quantum dynamics involving the time-reversal symmetry between solutions with outgoing and ingoing wave boundary conditions is pointed out to interpret photoionisation/photodetachment as half-scattering. This relationship is subsequently taken advantage to extend the formalism of Wigner–Eisenbud–Smith time delay in photoionisation/photodetachment. The measurability of time delay is accounted for in terms of a self-adjoint quantum operator that characterises it, even if there is no such operator for time itself. A few illustrative examples of theoretical and experimental studies of time delay are given to indicate outstanding advances made in this field in the last two decades.