Discussions of the Unruh effect are often confused by the unrealistic nature of the trajectory (acceleration ad infinitum) and by the invocation of accelerated observers. We present a formalism that allows the calculation of radiation emission from accelerated atoms and mirrors in time-dependent perturbation theory moving along asymptotically inertial trajectories. The description is unambiguously set in terms pertaining to the laboratory frame. In the limit of constant acceleration of infinite

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... duration one recovers Unruh's result. 1 The c-numbers α k are given in BCI. Transformation (24) would have to be implemented in the case of vanishing velocity B = 0 in order to get rid of the φ(0) term and provide the binding of the electron to the static course.