Spectral lines widths

The spectral line widths are related to the rate of the rotational motions, which average anisotropies in the g- and hyperfine matrices (Chapter 5), and to the rates of fluxional processes, which average nuclear positions in a radical. 

As the behavior of the spectral line width, 7710(1/77), can roughly be regarded as linear in 77 and the coefficient value 21n2 1.386 is close to 1.2, the approximation (4.3.38) holds workable for normal orientations even at AQ>>t]. 

The recoilless nuclear resonance absorption of y-radiation (Mossbauer effect) has been verified for more than 40 elements, but only some 15 of them are suitable for practical applications [33, 34]. The limiting factors are the lifetime and the energy of the nuclear excited state involved in the Mossbauer transition. The lifetime determines the spectral line width, which should not exceed the hyperfine interaction energies to be observed. The transition energy of the y-quanta determines the recoil energy and thus the resonance effect [34]. 57Fe is by far the most suited and thus the most widely studied Mossbauer-active nuclide, and 57Fe Mossbauer spectroscopy has become a standard technique for the characterisation of SCO compounds of iron. 

All spectra are due to the absorbance of electromagnetic radiation energy by a sample. Except for thermal (kinetic) energy, all other energy states of matter are quantized. Quantized transitions imply precise energy levels that would give rise to line spectra with virtually no line-width. Most spectral peaks have a definite width that can be explained in several ways. First, the spectral line-width can be related to the... 

Spectral line width varies inversely with the excited-state lifetime according to Heisenbergs principle, AT X A H = hi 2n, where AT is the lifetime of the excited spin state, h is Planck s constant, and AH is the effective width of the absorption signal. Excited-state lifetimes are subject to environmental (including chemical) influences. The resulting line-shape changes yield information about the chemical environment of the Mn atoms. Both spin-lattice and spin-spin relaxation mechanisms can contribute to the overall lifetime. 

Figure 14 Experimental 170 stationary NMR spectra for [170]-L-aianine, recorded at (A) 9.4, (B) 11.7, (C) 16.4 and (D) 21.6 T. Each spectral line width in frequency unit, SW, is also given.

Spectral line widths, as measured from peak-to-peak on the derivative of the ESR absorption curve, may vary from a few tenths of a gauss to nearly one hundred gauss depending on the rank of the coal (1, 2, 3, 8, 10, 11). For coals having carbon contents between 55 and 90%, peak-to-peak line widths range from 5.2 to —8.6. A gradual increase in line width with increasing carbon content is observed first this trend is... 

Solvent-Refined Coal. The solvent-refined coal (SRC 1) process (40) produces a low-sulfur, low-ash solid fuel from coal. Through the courtesy of L. Taylor, samples of SRC produced from five different feed coals were made available to us for ESR studies. Each of the five samples gave a strong ESR resonance near g=2 g values and spectral line widths are summarized in Table II. The g value and line width data, viewed collectively, suggest the presence of organic free radicals, with only minor interaction (except possibly for the Monterey sample) between the unpaired electrons and heteroatoms in the samples. 

Table II. ESR g Values and Spectral Line Widths for Selected Samples of Solvent-Refined Coal...

The effect of atmospheric gas on the emission of an LIB plasma [146] exhibits selfabsorption in He compared to Ar as a result of increased free atom populations in the outer regions of the plasma. Spectral line widths do not correlate well with atmospheric gas. This rules out Doppler effects as a major source of broadening in the laser-induced plasma. The use of a low pressure (ca. 1 torr) to examine the influence of this variable on the shock wave or secondary plasma revealed an increased emission intensity, which confirmed the assumption that the secondary plasma was excited by the shock wave. 

Atomic spectral lines have finite widths. With ordinary measuring spectrometers, the observed line widths are determined not by the atomic system but by the spee-trometer properties. With very-high-resolution spectrometers or with interferometers, the actual widths of spectral lines can be measured. Several factors contribute to atomic spectral line widths. 

The information from such experiments, of which there are now many examples(2,3), is important to our understanding of both dynamics and structure. First, since the dynamics of the initially excited state are reflected in spectral line widths, factors which control the rate of vibrational energy flow within molecules can be studied by recording spectra as a function of molecular structure. Fast randomization of this energy is a postulate of statistical unimolecular rate theories. On the... 

Ideally, the varied environment within the folded protein will generate unique chemical shifts for all of the nuclear spins. In practice, many of the protons (as well as other types of spins) in a protein show differences in chemical shift that are less than the spectral line width. These resonance lines are termed degenerate because it is not possible to resolve their individual spectral lines. In some cases, this degeneracy can be removed by increasing the dimensionality of the spectra. Multidimensional NMR experiments will be discussed in more detail later. 

The key point is the effect of molecular weight on the spectral density function. As the molecular size increases, the intensity of fluctuations with a frequency close to the zero quantum transitions also increases. Hence, the spin-spin relaxation rate increases as the molecular weight increases. This has two very important consequences. First, the spectral line width will increase as the molecular size increases. Consequently, the NMR spectra of larger proteins show increased degeneracy because of the increased number of resonances and the increased line width. The second consequence of the shortened lifetime of the excited state is a reduction in the efficiency by which magnetization can be passed from one nucleus to another... 

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