Incoherent measured intensity

The measured intensity can be spHt into coherent and incoherent contributions, as in the case of the scattering cross-sections... 

If an incoherent scatterer like CH4 is studied, the second term in Eq. 22 will be zero (fccoh = 0) nd the measured intensity will be proportional to... 

Figure 2.5 Measured scattering intensity for vitreous Si02 using Cu Ka radiation (corrected for absorption, polarization, and normalized to electron units see Ref. 4) (A) Coherent intensity I eu/N (B) incoherently scattered intensity.

Treatment of Intensity Data. After corrections for back-ground, polarization and absorption in the sample, the measured intensities were scaled to absolute intensities by the conventional methods. The coherent and incoherent scattering factors of the atoms in the sample were quoted from the literature (see each reference). 

For the NFS spectrum of [Fe(tpa)(NCS)2] recorded at 108 K, which exhibits a HS to LS ratio of about 1 1, a coherent and an incoherent superposition of the forward scattered radiation from 50% LS and 50% HS isomers was compared, each characterized by its corresponding QB pattern (Fig. 9.16) [42]. The experimental spectrum correlates much better with a purely coherent superposition of LS and HS contributions. However, this observation does not yield the unequivocal conclusion that the superposition is purely coherent, because in the 0.5 mm thick sample the longitudinal coherence predominates since many HS and LS domains lie along the forward scattering pathway. In order to arrive at a more conclusive result, the NFS measurement ought to be performed with a smaller ratio aJD on a much thinner sample. Such an experiment would require a sample with 100% eiuiched Fe and a much higher beam intensity. 

Two additional feature can be incorporated into Eqs. (7.32)—(7.35) the dipole orientation distribution and the concentration distribution in systems consisting of many dipoles. The orientation of the dipole with respect to the surface, described by angles Q = (8, ), affects E and all the other measurables derived from it.(33) Consider a concentration distribution of dipoles in both orientation and distance from the surface specified by C(0, , z). Since the dipoles all oscillate incoherently with respect to one another, the integrated intensity J due to this distribution is simply ... 

A semidilute solution [42] of high molecular weight deuterated polystyrene (Mw = 1.95 x 106 g/mole, Mw/M = 1.64) in dioctyl phthalate (DOP) at a volume fraction of 2.83% of polystyrene was measured by SANS at room temperature. A characteristic intensity behavior I(Q) was obtained after data correction (solvent incoherent scattering, empty cell scattering and usual background corrections, etc.) and was circularly averaged. The reduced I(Q) data was then fitted to the following form ... 

We shall conclude this chapter with a few speculative remarks on possible future developments of nonlinear IR spectroscopy on peptides and proteins. Up to now, we have demonstrated a detailed relationship between the known structure of a few model peptides and the excitonic system of coupled amide I vibrations and have proven the correctness of the excitonic coupling model (at least in principle). We have demonstrated two realizations of 2D-IR spectroscopy a frequency domain (incoherent) technique (Section IV.C) and a form of semi-impulsive method (Section IV.E), which from the experimental viewpoint is extremely simple. Other 2D methods, proposed recently by Mukamel and coworkers (47), would not pose any additional experimental difficulty. In the case of NMR, time domain Fourier transform (FT) methods have proven to be more sensitive by far as a result of the multiplex advantage, which compensates for the small population differences of spin transitions at room temperature. It was recently demonstrated that FT methods are just as advantageous in the infrared regime, although one has to measure electric fields rather than intensities, which cannot be done directly by an electric field detector but requires heterodyned echoes or spectral interferometry (146). Future work will have to explore which experimental technique is most powerful and reliable. 

Fig. 15. Basic equipment for measuring a nuclear inelastic scattering spectrum. Detector 1 measures the intensity of the incoherent nuclear forward scattering, which proceeds both elastically and inelas-tically detector 2 measures only the intensity of the coherent nuclear forward scattering, which proceeds elastically. Figure according to Ruffer and Chumakov (224).

Since, in HRS, there is no preferred orientation induced by an additional static field, there is the possibility of varying the experimental conditions in order to increase the number of independent observables. The number of theoretically possible independent observations, and hence the number of tensor components that can be obtained by HRS, is at most five. For parametric light scattering, this number is six, due to the possibility of distinguishing between the two optical fundamental fields [20]. The experimental difficulty has precluded the determination of this number of components. What is experimentally realistic in HRS is an additional depolarization measurement, apart from the classical measurement of the intensity of the second-order incoherent scattered light. The two measurements, the total intensity measurement and the depolarization ratio (or two intensity measurements, one with parallel and one with perpendicular polarization for fundamental and second harmonic), represent two independent observables and allow the experimental determination of two tensor components. For molecules of C2 symmetry, these are and P xxy resulting for the total intensity measurement in Eqn. (21),... 

The total-intensity hyper-Rayleigh scattering experiment basically consists of measuring the amount of incoherently scattered optical second harmonic (parallel and perpendicular output polarizations) versus a reference. When only this single measurement is done, only one independent tensor component can be obtained. For charge transfer molecules, this is generally approximated by P. The depolariza-... 

Finally, it should be noted that dephasing dynamics may also be investigated with temporally incoherent pulses [30-32]. To the extent that the two- and three-pulse Tj measurements described in the preceding depend upon the electric field correlation and not upon the intensity autocorrelations, femtosecond temporal resolution may be obtained with any broadband source. Spectral cross-relaxation and a variety of effects, however, can reduce the effectiveness of this technique. 

Single-molecule spectra as a function of laser intensity provided details of the incoherent saturation behavior and the influence of the dark triplet state dynamics [33]. Clear heterogeneity in the observed saturation intensity was observed indicating that the individual molecules experience modihcations in photophysical parameters due to differences in local environments. It was also possible to measure the linewidth of single pentacene molecules as a function of temperature in order to probe dephasing effects produced by coupling to a local phonon mode [33]. 

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