On the spontaneous radiative decay of a moving atom

We consider the relationship between the spontaneous radiative decay of an atom at rest and of an atom moving with a constant velocity. Based on the relativistic form, Aμjμ, of the field-current interaction we analyse two situations. In the first of them the radiative decay of a single atom is considered by using two different reference frames. In the second, a single reference frame is used to describe the radiative decay of two identical atoms, one of which is at rest in this frame and the other one moves with a constant velocity. Although in special relativity only the relative velocity between a source and an observer matters, there are subtle differences in the analysis of these situations: within the framework of the first situation one deals only with the Lorentz transformation, which is insensitive to whether exact or approximate atomic wave functions are used in the analysis, whereas the analysis of the second situation involves a gauge transformation which in general is not compatible with using approximate atomic wave functions. We have also shown that this gauge transformation can be used as a test for the accuracy of approximate atomic states obtained in atomic structure calculations