Convolution Problems in Time-Resolved X-Ray Diffraction

Abstract

Convolution problems in the time-resolved scattering of 10–1000-ps x-ray pulses are studied theoretically. The model system is a diluted solution of diatomic molecules A2 dissolved in an inert solvent. This system is submitted to a sub-picosecond laser pulse, which promotes the molecules A2 into an excited electronic state. The molecule then return into their ground state, passing through several intermediate electronic states. The effects of the finite duration of probing x-ray pulses on various x-ray signals are then examined in the frame of this model. Unbiased signals generated by very short x-ray pulses are explored first. Variations of a molecular geometry during this process are clearly visible in r-resolved, but are less explicit in q-resolved signals. The signals measured with x-ray pulses of a finite duration are studied next. Atomic motions remain detectable, but only if the x-ray pulses are shorter than or comparable to the times of a molecular dynamics. Here again, the r-resolved signals are more appropriate for monitoring the molecular dynamics than q-resolved signals. Finally, the effect of the insufficient temporal location of probing x-ray pulses with respect to that of exciting laser pulses is examined. It is shown that this last effect can be accounted for by simply replacing the true x-ray pulse intensity by another theoretically predicted intensity. The similarity of deconvolution techniques in spectroscopy and in time-resolved x-ray diffraction is strongly emphasized.