Homogeneous broadening linewidth

Therefore, the absorjDtion line is massively inlromogeneously broadened at low temperature. An inliomogeneous lineshape can be used to detennine the static or quasistatic frequency spread of oscillators due to a distribution of environments, but it provides no dynamical infonnation whatsoever [94, 95]. As T is increased to 300 K, the absorjDtion linewidth decreases and increases. At 300 K, the lineshape is nearly homogeneously broadened and dominated by vibrational dephasing, because fast dephasing wipes out effects of inliomogeneous environments, a well known phenomenon tenned motional narrowing [951. 

Unlike high-resolution NMR spectra of bulk solutions where NMR linewidths well below 1 Hz can be obtained routinely, NMR spectra of liquids permeating porous solids in most cases will not exhibit such a high spectral resolution. First of all, the interaction of liquid phase molecules with pore walls of the catalyst and rapid diffusion-driven intrapore transport will lead to a pronounced homogeneous broadening of the observed NMR lines. Smaller pore sizes and the presence of paramagnetic impurities in the solid material usually aggravate the situation and thus should be avoided. Another reason why NMR spectra of liquids in porous... 

FIGURE 4.2 Linewidth increase with temperature for an S = 1/2 system. The linewidth of a feature in the low-spin heme spectrum from cytochrome a in bovine heart cytochrome oxidase has been fit as a convolution of a constant component from inhomogeneous broadening and a temperature-dependent component from homogeneous broadening (Hagen 2006). (Reproduced by permission of The Royal Society of Chemistry.)... 

On the other hand, Schaefer ( ) has shown from selective saturation experiments of amorphous cis polyisoprene, crystalline trans polyisoprene, as well as carbon black filled cis polyisoprene, that the resonant lines are homogeneous. The linewidths in these cases are thus not caused by inhomogeneous broadening resulting from equivalent nuclei being subject to differing local magnetic fields. The results for these systems are thus contrary in part to what has been found here. 

FIGURE 5.5 (a) Components of the CARS signal. The last three terms in Equation 5.1 are plotted versus detuning A = C0p-co -O. O is the center frequency of a homogeneously broadened Raman line with linewidth F. The curves are calculated with an assumption that2 R = 1.2 = 0)- (b) Schematic of the FM CARS process. Solid curve, sum of the contribu-... 

As noted above, in their straightforward implementation, the Bloch equations correspond to the homogeneous broadening limit. To account for contributions to the linewidth that do not originate from the thermal environment, for example, radiative and intramolecular relaxation, we may replace in Eq. (18.49) by = Ad -T Aj where k is the combined rate of these other relaxation processes that will be taken constant in the following discussion. In what follows we focus on the width Ad which is associated with the thermal environment. 

Fig. 14. Schematic of selective excitation and ID exchange spectroscopy, (a) Typical pulse sequence with a soft selective pulse centered at pulsation a>s with a frequency dispersion AcoP <3C Aoj much smaller than the typical linewidth. After an evolution time te smaller or of the order of the spin-lattice relaxation time, a reading sequence of hard pulses that covers uniformly the whole broad line is applied, (b) Effect of a selective excitation on a homogeneously broaden line, (c) Selective frequency labeling of an inhomogeneously broaden line at the irradiation pulsation cos of the first soft pulse. For a soft n pulse, the magnetizations of all the spins that can exchange energy at this pulsation are reversed. By following the difference spectra between the spectra acquired at different evolution times te and the fully relaxed spectrum AS(te) — S(t -> oo) — S(te), limits or evaluation of the correlation time tc of the motion can be achieved.

As mentioned before, an increase in temperature activates low frequency modes of the matrix (phonons) or the molecule (librations) which lead to a broadening and a frequency shift of the homogeneous absorption line. In experiments with ensembles of molecules the homogeneous optical linewidth and its temperature dependence... 

In the case of inhomogeneous laser transitions, the whole line profile can be divided into homogeneously broadened subsections with the spectral width (for example, the natural linewidth or the pressure- or... 

It is generally accepted that the linewidth 6v (in cm ) of the same Raman mode, Wy, as observed from spontaneous Raman scattering is related to T2 by 6v = (ircT2) provided that the Raman line is homogeneously broadened (see, e.g., Laubereau and Kaiser, 1978). 

The intensity of ESR absorption relates to spin concentration, and spin susceptibility can also be measured using standard sample of known spin susceptibility. The g tensor depends upon the paramagnetic species present and its value is the fimction of the spin environment. For free electrons g = 2.00232. The linewidth peak to peak (A//pp) depends on the relaxation time. Homogeneously broadened lines have Lorentzian shapes, whereas inhomogeneously broadened lines have Gaussian shapes. In practice, a combination of both occurs. Normally the ratio of low field to high field is unity, but it can be greater. 

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