Resonances lifetime analysis

P.G. Hipes and A. Kuppermann, Lifetime analysis of high-energy resonances in three-dimensional reactive scattering. Chem. Phys. Lett., 133 1-7, 1987. 

Notice that this differs from the analysis of section II.B. Nevertheless, once S is represented by a direct part and a resonance part (in the form of either a product or a sum), the resonance lifetime or delay time is calculated from the energy derivative of the phase of the resonance part in a reasonably consistent way. 

A lifetime analysis of this kind requires a decomposition of either the element of the scattering matrix or, in some instances, its phase, into the resonance and direct components, and is therefore model-dependent. Nevertheless, it furnishes a very interesting characterization of the dynamic mechanism of the reactive process. In the H 4- H2 example considered, it clearly shows that the observed structure in the reaction probability curve of Fig. 1 is due to the simultaneous presence of direct and resonance contributions and of their quantum mechanical interference. The physical nature of the "trapping" of the system in the strong interaction region, leading to an increased lifetime, is, however, not elucidated by this analysis. Models for trappings of this kind will be discussed in section II.F. 

A unique situation is encountered if Fe-M6ssbauer spectroscopy is applied for the study of spin-state transitions in iron complexes. The half-life of the excited state of the Fe nucleus involved in the Mossbauer experiment is tj/2 = 0.977 X 10 s which is related to the decay constant k by tj/2 = ln2/fe. The lifetime t = l//c is therefore = 1.410 x 10 s which value is just at the centre of the range estimated for the spin-state lifetime Tl = I/Zclh- Thus both the situations discussed above are expected to appear under suitable conditions in the Mossbauer spectra. The quantity of importance is here the nuclear Larmor precession frequency co . If the spin-state lifetime Tl = 1/feLH is long relative to the nuclear precession time l/co , i.e. Tl > l/o) , individual and sharp resonance lines for the two spin states are observed. On the other hand, if the spin-state lifetime is short and thus < l/o) , averaged spectra with intermediate values of quadrupole splitting A q and isomer shift 5 are found. For the intermediate case where Tl 1/cl , broadened and asymmetric resonance lines are obtained. These may be the subject of a lineshape analysis that will eventually produce values of rate constants for the dynamic spin-state inter-conversion process. The rate constants extracted from the spectra will be necessarily of the order of 10 -10 s"F... 

Relaxation measurements provide a wealth of information both on the extent of the interaction between the resonating nuclei and the unpaired electrons, and on the time dependence of the parameters associated with the interaction. Whereas the dipolar coupling depends on the electron-nucleus distance, and therefore contains structural information, the contact contribution is related to the unpaired spin density on the various resonating nuclei and therefore to the topology (through chemical bonds) and the overall electronic structure of the molecule. The time-dependent phenomena associated with electron-nucleus interactions are related to the molecular system, and to the lifetimes of different chemical situations, for the resonating nucleus. Obtaining either structural or dynamic information, however, is only possible if an in-depth analysis of a series of experimental results provides sufficient data to characterize the system within the theoretical framework discussed in this chapter. 

Several molecules with 3 A. ground states have been studied by both microwave and far-infrared laser magnetic resonance they include O2, SO and SeO. In O2 the observed transitions are necessarily magnetic dipole, and they are frequently used to calibrate the sensitivity of a FIR laser magnetic resonance spectrometer. The other species have electric dipole transitions, and we shall illustrate the situation by describing the studies of SO carried out by Carrington, Levy and Miller [56], SO was also one of the first free radicals to be studied by pure microwave methods, which we will describe in chapter 10. The analysis of the magnetic resonance spectrum actually made use of the parameters determined earlier by pure microwave studies. SO is an easy radical to study experimentally since it is relatively unreactive and has a lifetime of several... 

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