SOJOURN-TIME APPROACH TO INTERACTION TIME IN QUANTUM SCATTERING - ONE-DIMENSIONAL SCATTERING WITH INTERNAL DEGREES OF FREEDOM

The system studied is a two-level particle whose translational motion is one dimensional and restricted to the half line (0,). The internal degrees of freedom of the particle are weakly coupled to the translational motion via a coupling including both adiabatic and nonadiabatic parts. We explore the idea of describing the interaction times of this scattering system in terms of Hermitian sojourn-time operators. Treating the coupling as a perturbation, we show that the first-order perturbation theory can be consistently formulated in terms of appropriate sojourn-time operators. The mean values of these operators give mean sojourn time (dwell time) of the particle in spatial regions or, more generally, in certain subspaces of the state space of the system. The perturbed S operator and also the effect of the perturbation on the change of observables due to the scattering are, in first-order approximation, fully expressible in terms of the sojourn-time operators. In particular, these operators fully determine the first-order approximation to the inelastic scattering probabilities. The relation to the case of scattering on the whole line (,) is briefly discussed. © 1990 The American Physical Society.