On the lifetime of the intermediate system in quantum-mechanical collisions

The “spin-clock” method proposed by Baz' to derive formulae for the duration of scattering processes in a stationary context is discussed. The formulae proposed by Baz' show discrepancies with the work of other authors, consisting of certain oscillatory terms. In other types of approach oscillatory terms occur in intermediate expressions, but a justification can then be given to eliminate there in the final result. It is shown that the oscillatory contributions of Baz' have a different origin: they arise from spurious reflection and transmission effects. Eliminating these, discrepancies are no longer present. In this context a problem is discussed which plays a role in all derivations of time delay in which incoming and outgoing waves are compared at a finite radius. Possible extensions of the corrected spin-clock method to time-dependent scattering are given together with their relation to other approaches. Only particle scattering from a spherically symmetric potential with finite range is considered.