Lorentzian peak

The full width at half height of these Lorentzian peaks is 2/x. One says that the individual peaks have been pressure or eollisionally broadened. 

Fig. 13. X-ray intensity profile with diffi action vector along qx (in the plane of layers) in the smectic X phase for the mixture of polyphilic compounds M70. The solid line through the data points is the smn of three Lorentzian peaks which are shown hy broken curves (Blinov et al. [44])...

Model Lorentzian Peaks. If all the terms on the right-hand side of Eq. (8.13) can be modeled by Lorentz curves, the integral breadth of the observed peak... 

Model Mixed Gaussian and Lorentzian Peaks. Even if one of the distributions must be modeled by a Gaussian and the other by a Lorentzian while the instrumental broadening is already eliminated, a solution has been deduced (Ruland [124], 1965). 

This logarithmic peak is much more gradual than the Lorentzian peak of the conventional transmission resonance of (13.11). It can, however, be sharp as well. 

The oxygen nonstoiehiometry as well as the redox properties of Co-, Mn- and Fe-based perovskites was investigated by means of O2-TPD and H2-TPR and XPS teehniques. The amounts of O2 released dining O2-TPD were calculated after deconvolution of the O2 desorption curves using Lorentzian peak shape and they are reported in Table 2. 

This represents a single Lorentzian peak near co0. It shows how it is possible that more rapid perturbations lead to a narrower line. ... 

Before we see how the spectrum of Fig. 21.11 emerges from Fig. 21.12, let us try a simpler case, the 6sl6d 1D2 —> 6p1/216d5/2 ICE transition, which exhibits a Lorentzian peak at v2 =13.3.16 Since the peak falls at the center of the (vbdB v2d) overlap integral the cross section is proportional to A2, which should thus have a maximum at v2 = 13.3. Inspecting Fig. 21.14 we can see that the 6p1/216d5/2 state lies on the last full branch of the v2, v3 curve, from v3 = 6.85 to v3 = 6.98 and v2 = 13 to v2 = 14. This branch of the curve of Fig. 21.14 is almost parallel to the v2 axis and lies at v3 6.9 where the normal of the quantum defect surface points in the direction except at v2 13.3 where it points predominantly in the v2 direction. In other words the normal to the quantum defect surface also tells us that A2 is... 

Naively one could think that scattering on weak barriers cannot possibly yield a sharp peak in G(eo, T). Indeed, the transmission probability as a function of e does not have any peak at e = eo, in contrast to the case of resonant tunneling. At high T, G(eo,T) is a weakly oscillating (with a period A) function of eo- The only difference with the non-interacting case is an enhanced amplitude of the oscillations. In fact, however, the interaction-induced vanishing of the transmission probability at ep for T = 0 does lead to a narrow Lorentzian peak of G(eo,T), provided that T is low enough and the barriers are not too asymmetric. 

It is clear that the unmistakable resonance fingerprint provided by a narrow Lorentzian peak in the integral cross section (ICS) will be rare for reactive resonances in a collision experiment. However, a fully resolved scattering experiment provides a wealth of data concerning the reaction dynamics. We expect that the state-to-state differential cross sections (DCS) as functions of energy can be analyzed, using various methods, to reveal the presence of reactive resonances. In the following subsections, we discuss how various collision observables are influenced by existence of a complex intermediate. Many of the resonance detection schemes that have been proposed, such as the use of collision time delay, are purely theoretical in that the observations required are not currently feasible in the laboratory. Nevertheless, these ideas are also discussed since it is useful to have method available... 

Figure 4.9 provides a whole view of the Q-matrix eigenvalues [qAE) and Tr Q(E), calculated for Hef1/ ") using the HSCC equations, in an energy region between the thresholds ofHe+(n = 4) = —0.125 a.u. and He+(n = 5) = -0.08 a.u. [69]. Some Lorentzian peaks stand out distinctly and no complicated analysis appears to be necessary for them. On the other hand, many... 

Fig. 15 Small-angle X-ray scattering curves of poly(L-arginine) retinoate (a), poly(L-his-tidine) retinoate (b) and poly(L-lysine) retinoate (c). The dashed lines are fits using a Lorentzian peak profile. Repeat units are 3.62 nm, 3.27 nm, and 3.10 nm. Reprinted with permission from [142]. Copyright 2000 American Chemical Society...

The Fourier transform converts the FID into a Lorentzian peak with absorptive lineshape (after phase correction). The full width of this peak at one half of the peak s height (the linewidth ) is inversely related to the decay time constant of the FID, ... 

It can be shown that the width at half-height of a Lorentzian peak is given by A1/2 = 2.s and the area by jt As note this depends on both the height and the width. 

The peakshape in the frequency domain relates to the decay curve (or mechanism) in the time domain. The time domain equivalent of a Lorentzian peak is... 

As shown in Fig. 3, the decay time 7 of the FID is related to the half-width of the Lorentzian peak. The quantity 1/7 gives a measure of the rate at which the My component decays due to randomization of the bunched individual magnetic moments on the precessional cone. This dephasing involves no energy change and is caused by spin-spin... 

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