Linewidth and lifetime of atomic levels and the time evolution of spectra and coincidence spectra

The time-dependent theory of an atomic cascade decay process is discussed. We show that it is useful to measure the spectra of the emitted particles (electrons or photons) as a function of time and introduce time-dependent spectra and time-dependent coincidence spectra. The analysis reveals that there are several timescales involved in the atomic cascades and in the respective spectra. The work prepares the ground for the discussion of molecules, clusters, and solids, where the nuclear dynamics strongly participate in the cascade decay process making it much more complex.