Experiments with Finite Delays

Equation 1 was derived assuming that the nuclear spin magnetizations are at thermal equilibrium values prior to the start of the presaturation. In practice, due to time constraints on the instrument, this condition may not usually be reahzed and the nuclear spin magnetization can generally be in a quasiequilibrium state prior to presaturation. If (tj + t) is the delay between two consecutive 90° observe pulses, where t is the presaturation period and fa is the time delay before presaturation (this includes the data acquisition time for the previous pulse), then the appropriate expressions for STD and for control NMR spectra are given by  

In the above expressions, the subscript F refers to the full relaxation and exchange matrices that include the P2 and P2 protons since their magnetizations do not experience rf saturation during in the on-resonance saturation experiment and during ti + t in the off-resonance irradiation experiment (control spectrum). Hence, experience coupled recovery with the rest of the protons during these periods. The subscript r refers to the reduced matrix containing elements for I, I, PI, and PI extracted from the full matrix. We have implemented the above expressions as an option in the CORCEMA-ST program. 

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An electronic or vibrational excited state has a finite global lifetime and its de-excitation, when it is not metastable, is very fast compared to the standard measurement time conditions. Dedicated lifetime measurements are a part of spectroscopy known as time domain spectroscopy. One of the methods is based on the existence of pulsed lasers that can deliver radiation beams of very short duration and adjustable repetition rates. The frequency of the radiation pulse of these lasers, tuned to the frequency of a discrete transition, as in a free-electron laser (FEL), can be used to determine the lifetime of the excited state of the transition in a pump-probe experiment. In this method, a pump energy pulse produces a transient transmission dip of the sample at the transition frequency due to saturation. The evolution of this dip with time is probed by a low-intensity pulse at the same frequency, as a function of the delay between the pump and probe pulses.1 When the decay is exponential, the slope of the decay of the transmission dip as a function of the delay, plotted in a log-linear scale, provides a value of the lifetime of the excited state. 

Bennett et al. have given a thorough discussion of SEDRA/RFDR-type experiments in ref. 104, where they covered influences from finite pulses, insufficient proton decoupling, and multi-spin interactions, and introduced a modified version of the basic RFDR sequence with delays of duration kr incorporated between sets of four tt pulses (see Fig. 2Id). This modification recouples weak dipolar coupling interactions only at the conditions n/kyjJt, which avoids the conditions (o A =znu>r) if n/k is not an... 

Figure 9.12 The ground and excited potentials for Nal with the localized state created by fs UV excitation shown both initially and as it moves. Right panel the probe signals for Na at a finite separation from I and for a Na atom far away as a function of the delay between the pump and probe pulses [adapted from T. S. Rose, M. J. Rosker, and A. H. Zewail, J. Chem. Phys. 88, 6672 (1988) see also Zewail (1996) and C. Jouvet et at., J. Phys. Chem. 101, 2555 (1997)]. This and similar experiments provide a direct experimental demonstration of the localized region of the non-adiabatic transition. It took over 50 years for the theoretical ideas of Landau and Zener to have this direct experimental test.

While both populations are equivalent in principle, being related by a unitary transformation, one of them may be more clo.sely related to experiment than the other. For example, if there are dipole. selection rules forbidding the optical transition to or from a subset of the interacting electronic states, these selection rules are usually obeyed to a much larger extent in the diabatic basis than in the adiabatic ba.si.s. Then the diabatic electronic populations are monitored via the intensities of spontaneous and induced emission (the adiabatic populations may be more relevant if the optical transition takes place within the interacting manifold). More specifically, in the limit of ideally short pump and probe pulses the time-resolved pump-probe signal as a function of the delay time has been shown to be proportional to the diabatic population, equation (51). For the more realistic case of finite pulse durations the situation is more complex. In the present article we leave these problems aside and focus on the purely intramolecular aspects of the vibronic dynamics. The various aspects associated with their detection in real time have been surveyed in a recent review article. ... 

UV irradiation leads to a cis-trans isomerization reaction. Since the rate of this isomerization reaction is finite, it is observed in experiments that the time of incidence of the laser pulse is not identical with the time of primary radical formation, but there is a certain delay, usually in the order of microseconds. 

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