Duration of x-ray Raman scattering

There has recently been much interest in using the notion of a duration tim e to analyze resonant x-ray Raman scattering (RXS) of atoms, molecules, and solids. This notion implies a selection of processes with different time s cales responsible for the formation x-ray Raman spectra, and has been usefu l for actual predictions of various phenomena associated with RXS and that subsequently have been experimentally verified. However, the notion of a du ration time for the x-ray scattering event can also have some paradoxical c onsequences, as when comparing the RXS duration with the relaxation time of the wave packet evolution in the case when the inverse detuning of the exc itation energy is shorter than the time of flight or the lifetime of the co re excited state. We present here a solution of this contradiction and give a detailed analysis of the notion of the duration time for RXS. It is show n that this time is complex and consists of two qualitatively different con tributions. The first originates in the irreversible decay of the core exci ted state, while the imaginary part is caused by a reversible dephasing in the time domain. We investigate also the evolution of the wave packets of b ound and dissociative states to stationary distributions. The theoretical a nalysis is accompanied by numerical examples of the time evolution of the w ave packet in bound and dissociative core excited states of the N-2 and HCl molecules. [S1050-2947(99)06101-6].