Measurement of linewidths

Consider now predissociation of the final state of a transition (upper state in absorption or lower state in emission). It is often the upper state of an absorption transition that is predissociated, but the effect of the predissociation on spectral linewidths is identical to the case when the lower state of an emission transition is predissociated (for example, the B2E+ — A2E+ system of OH where the A state is strongly predissociated). In either case, the spectrum consists of diffuse lines (see Fig. 7.15 for predissociation of the Se2 B0+ state). The predissociated state obtains its diffuse character from the continuum state. 

To treat predissociation quantitatively, precise measurements of the width (full width at half maximum, FWHM, or T, often misleadingly referred to as the half-width) of each rotational level are necessary. In the absence of Doppler broadening, the lineshape ora(E) is usually Lorentzian, 

Molecule Ref. Predissociated State Predissociating State Cmax (cm ) Experimental (except Se2,BeH)6 (.Xv Xe)2 Differential Pranck-Condon Factor (cm) He Electronic Matrix Element (calc.) Origin of the Interaction 

For E = Er (the energy including the predissociation-induced energy shift, called the resonance energy), the absorption has its maximum value, aa(Er) = 

In typical experiments, only strong predissociations that result in a nonra-diative lifetime much shorter than the radiative lifetime can be detected by line broadening, since the usual radiative lifetime of 10 8s corresponds to a width of only 5 x 10-4 cm-1. Doppler-free spectroscopic techniques have made it possible to measure extremely small predissociation linewidths (Carre, et al., 1980 Carrington, et al., 1978). 

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High-resolution measurement of linewidths of transitions to individual eigenstates. 

This type of estimate of expected decoherence rates could, in principle, be carried out for similar simple systems where the randomness in the interaction with an environment is known from spectroscopic measurements of linewidths. It is valid as long as the measuring probes do not by themselves introduce additional perturbations. The diffraction data mentioned above for H - H dimers in KHCOa [Fillaux 2003 (a)] are results of elastic neutron interactions, which is a particularly soft way of probing delicate quantum states in condensed matter. 

A second group of techniques may be called lineshape analysis. Simple methods entail the measurements of linewidths or second moments as a function of temperature. More sophisticated methods involve the analysis or the model fitting of spectral lineshapes. A prominent method is ID lineshape analysis for deuterium-labeled polymers, which is sensitive to motions in the frequency range of lO -lO s (149). The 2D wideline separation NMR (WISE) experiment permits correlation of the high resolution spectrum with the wideline spectrum, which provides dipolar information (11,150). The linewidth is a function of the frequency of the polymer motion relative to the time scale of dipolar couplings. 

Rotational correlation times measured in sodium dodecyl, octyl and hexadecyl sulfate. ) Measurements of linewidth in (C4p9)3N with and without O2 being present. 

Propyl, phenylethyl phosphoramidates give similar spectra. Several related radicals reported. Measurement of linewidths with change of concentration of surfactant. Measurement of spin exchange with Ni. ... 

EPR Measurement of linewidth as a function of alignment in liquid crystals 84Bal2... 

Relaxation data of the quadrupolar halogens are directly obtained from pulsed NMR studies, although most data on T2 are from measurements of linewidth or from peak-to-peak distances of the first derivative of absorption curves. Using pulse methods the lower limit of Tj and T2 depends on the dead time of the spectrometer. Presently the practical limits appear to be ca. 10 ys. A number of the available relaxation data on Cl, Br, and I compounds have been determined through the effects of the halogen relaxation on the relaxation of directly bonded spin 1/2 nuclei through modulation of scalar interaction this mechanism is commonly termed "scalar relaxation of the second kind. Very short... 

Light sources can either be broadband, such as a Globar, a Nemst glower, an incandescent wire or mercury arc lamp or they can be tunable, such as a laser or optical parametric oscillator (OPO). In the fomier case, a monocln-omator is needed to achieve spectral resolution. In the case of a tunable light source, the spectral resolution is detemiined by the linewidth of the source itself In either case, the spectral coverage of the light source imposes limits on the vibrational frequencies that can be measured. Of course, limitations on the dispersing element and detector also affect the overall spectral response of the spectrometer. 

The absolute measurement of areas is not usually usefiil, because tlie sensitivity of the spectrometer depends on factors such as temperature, pulse length, amplifier settings and the exact tuning of the coil used to detect resonance. Peak intensities are also less usefiil, because linewidths vary, and because the resonance from a given chemical type of atom will often be split into a pattern called a multiplet. However, the relative overall areas of the peaks or multiplets still obey the simple rule given above, if appropriate conditions are met. Most samples have several chemically distinct types of (for example) hydrogen atoms within the molecules under study, so that a simple inspection of the number of peaks/multiplets and of their relative areas can help to identify the molecules, even in cases where no usefid infonnation is available from shifts or couplings. 

The sinc fiinction describes the best possible case, with often a much stronger frequency dependence of power output delivered at the probe-head. (It should be noted here that other excitation schemes are possible such as adiabatic passage [9] and stochastic excitation [fO] but these are only infrequently applied.) The excitation/recording of the NMR signal is further complicated as the pulse is then fed into the probe circuit which itself has a frequency response. As a result, a broad line will not only experience non-unifonn irradiation but also the intensity detected per spin at different frequency offsets will depend on this probe response, which depends on the quality factor (0. The quality factor is a measure of the sharpness of the resonance of the probe circuit and one definition is the resonance frequency/haltwidth of the resonance response of the circuit (also = a L/R where L is the inductance and R is the probe resistance). Flence, the width of the frequency response decreases as Q increases so that, typically, for a 2 of 100, the haltwidth of the frequency response at 100 MFIz is about 1 MFIz. Flence, direct FT-piilse observation of broad spectral lines becomes impractical with pulse teclmiques for linewidths greater than 200 kFIz. For a great majority of... 

After the signal emerges from the lock-m amplifier it still contains a considerable amount of noise. Most of the noise contributions to the signal can be eliminated by passing the signal tlirough a low-pass filter. The filter tune constant is a measure of the cutoff frequency of the filter. If accurate linewidth and g-factor... 

Suppression of the tme diagonal peaks by double-quantum filtering (DQF-COSY) may resolve such problems. Finally, quantitative measurements of the magnitude of the coupling constants is possible using the Z-COSY modification, These experiments ate restricted to systems of abundant spins such as H, and which have reasonably narrow linewidths. 

S. S. H. Naqvi, S. M. Caspar, K. C. Hickman, and J. R, McNeil. A Simple Technique for Linewidth Measurement of Gratings on Photomasks. Proc. SPIE. 1261, 495, 1990. K.P. Bishop, S.M. Caspar, L.M. Milner, S.S.H. Naqvi, and J.R, McNeil, rasterization using Scatterometry. Proc. SPIE. 1545, 64, 1991. These papers discusses a simple application of scattering from surhices that are intentionally patterned. 

To make accurate measurements of the integrated absorption associated with such narrow lines requires that the linewidth of the radiation source be appreciably smaller than that of the absorption line. In practice, this could be achieved with a continuum source only if expensive instrumentation of extremely high resolving power were used, and it is doubtful whether conventional photomultiplier detectors would be sufficiently sensitive at the resulting low radiation intensities. An alternative arrangement is to... 

The quantification of an NOE amounts to determining the volume of the corresponding cross peak in the NOESY spectrum. Since the linewidths can vary appreciably for different resonances, cross-peak volumes should in principle be determined by integration over the peak area rather than by measuring peak heights. However, one should also keep in mind that, according to Eq. (1), the relative error of the distance estimate is only one sixth of the relative error of the volume determination. Furthermore, Eq. (1) involves factors that have their origin in the complex internal dynamics of the macromolecule and are beyond practical reach such that even a very accurate measurement of peak volumes will not yield equally accurate conformational constraints. 

Figure 26 shows the dispersion curve of the Kr monolayer obtained from a large number of spectra like those in Fig. 25. The hybridization splitting around the crossing with the substrate Rayleigh wave (solid line) is clearly observed. Also the predicted tiny frequency upshift close to the T point due to the coupling to the substrate vibrations is seen. The observed linewidth broadening is also shown in Fig. 26. As a measure of the broadening, the quantity Ae = [( ) — with dE the FWHM of the major loss feature...

If a S> 1, collective effects play an important role and the light scattering is no longer caused by individual electrons but by electron density fluctuations 280), Jn this case the spectrum shows a central line at Xq and two narrow lines located symmetrically about Xq, at a distance governed by the electron plasma frequency. The linewidth is smaller than in the case X < 1 and is determined rather by the thermal motion of the ions, not that of the electrons. The line shape depends on the ratio of electron to ion temperatures. Therefore, a measurement of the shape and width of this central line allows, under certain assumptions, a direct determination of the ion temperature. 

This method is specially suited for measurements of closely spaced Zeeman or Stark splitting and fine and hyperfine structures, which are separated only within their doppler linewidth 5 ). 

The spectrum obtained by FT of the whole train of decaying echoes consisfs of a series of spikelets separated by the frequency vcpMG = l/ra. The envelope of these sidebands is defined by the second-order quadrupolar CT lineshape under MAS. The linewidth of each spikelet is determined by the true transverse relaxation time (T2) of the material, which is a measure of the decay time of the amplitude of the echoes in the... 

Accuracy of the radiofrequency measurements of the classic 2S — 2P Lamb shift [15, 16, 23, 24, 25] is limited by the large (about 100 MHz) natural width of the 2P state, and cannot be significantly improved. New perspectives in reducing the experimental error bars of the classic 2S — 2P Lamb shift were opened with the development of the Doppler-free two-photon laser spectroscopy for measurements of the transitions between the energy levels with different principal quantum numbers. Narrow linewidth of such transi-... 

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