Resonance lines, half-width

Fig. 2.7 Excitation resonance broadening of a two-level system with increasing laser radiation intensity (w is the field frequency, ujo is the central transition frequency, F = jTi is the homogeneous spectral-line half-width, and G is the saturation parameter).

It would appear that measurement of the integrated absorption coefficient should furnish an ideal method of quantitative analysis. In practice, however, the absolute measurement of the absorption coefficients of atomic spectral lines is extremely difficult. The natural line width of an atomic spectral line is about 10 5 nm, but owing to the influence of Doppler and pressure effects, the line is broadened to about 0.002 nm at flame temperatures of2000-3000 K. To measure the absorption coefficient of a line thus broadened would require a spectrometer with a resolving power of 500000. This difficulty was overcome by Walsh,41 who used a source of sharp emission lines with a much smaller half width than the absorption line, and the radiation frequency of which is centred on the absorption frequency. In this way, the absorption coefficient at the centre of the line, Kmax, may be measured. If the profile of the absorption line is assumed to be due only to Doppler broadening, then there is a relationship between Kmax and N0. Thus the only requirement of the spectrometer is that it shall be capable of isolating the required resonance line from all other lines emitted by the source. 

In a Mdssbauer transmission experiment, the absorber containing the stable Mdssbauer isotope is placed between the source and the detector (cf. Fig. 2.6). For the absorber, we assume the same mean energy q between nuclear excited and ground states as for the source, but with an additional intrinsic shift A due to chemical influence. The absorption Une, or resonant absorption cross-section cr( ), has the same Lorentzian shape as the emission line and if we assume also the same half width , cr( ) can be expressed as ([1] in Chap. 1)... 

Fig. 10. The ESR signal produced at various points on the resonant line in a magnetic field modulated spectrometer. The vertical magnetic field modulation interacts with the bell-shaped adsorption curve [F(H)1 to produce the horizontal ESR signal. Here AH is the half amplitude line width and Hu is the center of resonance (S3).

Load the proton spectrum of peracetylated glucose D NMRDATA GLUCOSE 1D H GH 002999,1R and expand a methyl resonance. From the Analysis pull-down menu choose the Linewidth option. With the cursor in Maximum Cursor mode, select a resonance line by clicking the left mouse button. With the cursor set on the top of the peak, click the right mouse button. A horizontal line indicates the intensity at half height and the corresponding line width (in Hz) will appear below the title bar. 

The first 27A1 MAS NMR study of zeolites was carried out by Freude and Behrens (151). They measured, first, chemical shifts and half-widths of signals from stationary samples of zeolites Na-A, Tl-A, Na-Y, and Tl-Y at 16 MHz. For MAS frequencies of vR such that vR > Vq/vl the central line of the 27A1 resonance is reduced to about j of its original value. Freude and Behrens next calculated the quadrupole frequencies vQ and shifts of the center of gravity of each line due to the quadrupole interaction, i.e., vQ = (v - vL)/vL at 70 MHz. Then, apparent line positions and line widths, S and <5v 2MAS, were measured experimentally using MAS at 70 MHz. The corrected chemical shift value at 70 MHz was then calculated from the relationship <5, = 5ex — <5q. They were several ppm different from the apparent values (see Table XII). 

The width AH0 of the resonance absorption curve measured at half peak power - the 3 dB resonance line width - should in general be as small as possible since this implies a narrow range of frequencies over which strong interaction with the ferrite can occur however, there are certain broad-band applications where this would not be the requirement. There are two main contributions to the linewidth ... 

The cavity is tuned by maximizing the atomic transfer rate. By this way, the cavity center frequency equals Fc within about 25% of the cavity resonance half-width. The slow variation of the MW power through the linewidth shifts the line in direction of the cavity center frequency. Since the cavity has a rather low quality factor, this shift is at the worst 500 Hz. Due to thermal drift, the cavity tuning may vary at the time scale of an hour, and yield a time-dependent 500 Hz systematic. 

Breit-Wigner resonances have Lorentzian line shapes /bw( ) = [( — l res)2+(Wres/2)2] and are symmetrical in E (where W is the width of the resonance at half-height, see Section 2.1). In contrast, Fano83 resonances have a different lineshape ... 

It is customary to keep the frequency constant while the field B is varied. At the commonly used frequency of 9.5 GHz (known as X-band microwave radiation and thus giving rise to X-band spectra) resonance occurs at a magnetic field of 0.34 T. Disturbances again cause a band of finite width, characterised by the line width at half height (ABi/2) again dipole-dipole interactions of the spins is a reason of the width of the resonance lines. 

From the simpler resonance line-shape and H/D-exchange analysis to the more complex studies of inherent dynamics, occurring on various time scale of motion, NMR remains a good choice to investigate protein flexibility and plasticity. If linebroadening due to exchange and inhomogeneity is minimized (or completely eliminated), then half-width, Aom, of a line becomes proportional to R, the transverse relaxation rate constant. 

The width of a resonance signal is related to the lifetime of a given magnetic state. The reciprocal of the half-width at half-height is the transverse relaxation time 7 . The line width is related to the exchange lifetime. 

The real part of this function is proportional to the absorption signal A((o), and the imaginary part to the dispersion signal D(ca) defined in (2.2.26) (cf. Fig. 2.2.6). The absorption signal is a resonance line with a full width at half height of = 2/72. The shorter the Ti, the faster the time-domain signal /(r) decays to zero and the wider the resonance line F(w) becomes. 

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