The behavior of uniformly accelerated detectors in the Minkowski and Rindler vacua is analyzed when the detector is coupled to a scalar field during a finite amount of time $T$. We point out that the logarithmic ultraviolet divergences reported in the literature are due to the instantaneous switching of the detector. We explicitly show this by considering a detector switched on and off continuously. The usual Planckian spectrum for the excitation probability is recovered in the limit $T\to +\infty$.

• Received 17 June 1993

DOI:https://doi.org/10.1103/PhysRevD.48.3731