Negative absorption dispersion

The phase-twisted peak shapes (or mixed absorption-dispersion peak shape) is shown in Fig. 3.9. Such peak shapes arise by the overlapping of the absorptive and dispersive contributions in the peak. The center of the peak contains mainly the absorptive component, while as we move away from the center there is an increasing dispersive component. Such mixed phases in peaks reduce the signal-to-noise ratio complicated interference effects can arise when such lines lie close to one another. Overlap between positive regions of two different peaks can mutually reinforce the lines (constructive interference), while overlap between positive and negative lobes can mutually cancel the signals in the region of overlap (destructive interference). 

There are generally three types of peaks pure 2D absorption peaks, pure negative 2D dispersion peaks, and phase-twisted absorption-dispersion peaks. Since the prime purpose of apodization is to enhance resolution and optimize sensitivity, it is necessary to know the peak shape on which apodization is planned. For example, absorption-mode lines, which display protruding ridges from top to bottom, can be dealt with by applying Lorentz-Gauss window functions, while phase-twisted absorption-dispersion peaks will need some special apodization operations, such as muliplication by sine-bell or phase-shifted sine-bell functions. 

The antiphase doublet (Fig. 6.14(c)) is dispersive because /-coupling evolution to the antiphase state moves the vectors by 90°, from the +x axis to the +/ and —/ axes. This dispersive antiphase doublet can be phase corrected by moving the reference axis from the +x axis to the +/ axis (90° zero-order phase correction). Now the C = a peak is positive absorptive and the C = ft peak is negative absorptive (Fig. 6.15) and the central 12CH3l peak is pure dispersive because the vector is on the -hx/ axis and the reference axis is now +y (90° phase error). 

Fig. 4.7 Illustration of the effect of a phase shift of the time domain signal on the spectrum. In (a) the signal starts out along x and so the spectrum is the absorption mode in the real part and the dispersion mode in the imaginary part. In (b) there is a phase shift, , of 45° the real and imaginary parts of the spectrum are now mixtures of absorption and dispersion. In (c)the phase shift is 90° now the absorption mode appears in the imaginary part of the spectrum. Finally in (d) the phase shift is 180° giving a negative absorption line in the real part of the spectrum. The vector diagrams illustrate the position of the signal at time zero.

This means that the real part of the spectrum shows a dispersion lineshape. On the other hand, if the magnetization is advanced by nil, 0 = 0sig - 0rx = nil - 0 = nil and it can be shown from Eq. [1] that the real part of the spectrum shows a negative dispersion lineshape. Finally, if either phase is advanced by n, the result is a negative absorption lineshape. 

For transitions between bound states, the oscillator strength is a fundamental new quantity which quantum mechanics introduces in dispersion theory. We now have not only one characteristic frequency vq but a whole series of transition frequencies Vjk, and the presence, not only of absorption terms, but also of negative absorption terms due to stimulated emission. The theory of Kramers [130] was checked experimentally by Ladenberg and Kopfermann [131] for a line in the spectrum of Ne. 

Although this eliminates negative contributions, since the imaginary part of the spectrum is also incorporated in the absolute-value mode, it produces broad dispersive components. This leads to the broadening of the base of the peaks ( tailing ), so lines recorded in the absolute-value mode are usually broader and show more tailing than those recorded in the pure absorption mode. 

Peaks in homonuclear 2D /-resolved spectra have a phase-twisted line shape with equal 2D absorptive and dispersive contributions. If a 45° projection is performed on them, the overlap of positive and negative contributions will mutually cancel and the peaks will disappear. The spectra are therefore presented in the absolute-value mode. 

According to F. P. le Roux, like all vapours with a large selective absorption, iodine has an anomalous dispersion since it increases with a fall of temp., being about 0 06 from A. Hurion s measurements—approximately as large a negative number as glass is positive. The atomic refraction of solid iodine is 24-5 by the //.-formula, and 14-12 by the /t2-formula. 

This means that the molar extinction coefficients of the two enantiomers (e, and er) are unequal in circularly polarized light. These differences in absorption (e, and er) can be measured as a function of wavelength, and the curves obtained are called circular dichroism curves. They have positive or negative signs (Cotton effect) just as for optical rotatory dispersion curves. 

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