Line intensities saturation effects

The intensity of a Mossbauer spectrum depends not only on the recoil-free fractions of the source and the absorber and on the number of absorbing nuclei, but also on the linewidth of the absorption lines and on whether or not saturation effects occur. The following approximate expression is valid for relatively thin absorbers [17] ... 

This is so when absorbers are thin and when the lines are broader than the natural linewidth. For heavier samples, saturation effects come into play. In case of a sextet, the factor b, in (5-7) forms the reason that the outer peaks are more affected than the inner peaks, with the result that the line intensity ratios become lower than the expected ratio of 3 1. 

This situation corresponds to the well-known saturation effect in the emission of most gas laser transitions, where, for the same reason, fewer upper-state molecules can contribute to the gain of the laser transition at the center of the doppler-broadened fluorescence line than nearby. When tuning the laser frequency across the doppler-line profile, the laser intensity therefore shows a dip at the centerfrequen-cy, called the Bennet hole or Lamb dip after W.R. Bennet who discovered and explained this phenomen, and W.E. Lamb 2) who predicted it in his general theory of a laser. 

Carbon-13 NMR Spectroscopy. High resolution 13C NMR spectra of maltenes, bitumen, and liquid products taken up in a 1 2 mixture of CDC13 were obtained on a Varian XL-100-15 FT spectrometer equipped with a V-4412 probe and a 2.5 mega word disc. A pulse angle of 45° and a repetition period of 60 s were selected to avoid saturation of any nonprotonated carbons. Gated decoupling was also employed to suppress NOE effects in the line intensities. These precautions have been shown for mixtures of model compounds to minimize error in integrated line intensities to less than 10% (3). 

Care must be taken to avoid saturation effects when measuring the oscillator strengths of intense MD transitions [126]. It has been assumed that MD oscillator strengths are rather insensitive to the site symmetry of a particular rare earth ion [127], and this may be the case for some particular transitions. However, the ED contribution to the zero phonon line intensity of an ion at a noncentrosymmetric site may be comparable to, or greater than the MD contribution, so that the measured intensity arises from both contributions. 

Measurements by photographic photometry require careful calibration due to the nonlinear response of photographic plates saturation effects can lead to erroneous values. Line profiles can be recorded photoelectrically, if the stability of the source intensity and the wavelength scanning mechanism are adequate. Often individual rotational lines are composed of incompletely resolved spin or hyperfine multiplet components. The contribution to the linewidth from such unresolved components can vary with J (or TV). In order to obtain the FWHM of an individual component, it is necessary to construct a model for the observed lineshape that takes into account calculated level splitttings and transition intensities. An average of the widths for two lines corresponding to predissociated levels of the same parity and J -value (for example the P and R lines of a 1II — 1E+ transition) can minimize experimental uncertainties. A theoretical Lorentzian shape is assumed here for simplicity, but in some cases, as explained in Section 7.9, interference effects with the continuum can result in asymmetric Fano-type lineshapes. 

Another nonlinear technique that is potentially applicable to thermometric measurements is DPWM [7,9]. Por instance, a Boltzmann plot constructed out of the relative line intensities of a DPWM spectrum can lead to temperature predictions that can be as accurate as CARS in some cases. An alternative method is to fit theoretical simulations to the experimental spectrum. Nonetheless, the versatility of CARS is not equaled by DPWM. In effect, single pulse measurements seems to be limited to some radical species and mode fluctuations of conventional lasers perturb the data severely. To avoid troubles with such laser intensity fluctuations, saturated DPWM is often employed, but the difficulties of spectral S5mthe-sis remain a serious hindrance to a major role of DPWM thermometry. 

Wg). A second advantage of ST resonance over ENDOR is that when both RF fields are sufficiently strong to completely saturate nuclear transitions the EPR desaturation becomes independent of Wj.. Consequently, the line intensities are no longer determined by the relaxation behaviour of the various nuclei, but rather reflect the number of nuclei involved in the transition. Finally, ST also has the advantage of higher resolution because the effective saturation of nuclear transitions results in smaller observed linewidths compared to ENDOR. 

Fig. 3.7 Curves illustrating the changes in the relative intensity of two hyperfine lines caused by saturation effects (a) with change in recoilless fraction, (b) with change in absorber thickness.

The Bloch equations (Eq. 5) can be solved under different conditions. The transient solution yields an expression for 0-22 (0> time-dependent population of the excited singlet state S. It will be discussed in detail in Section 1.2.4.3 in connection with the fluorescence intensity autocorrelation function. Here we are interested in the steady state solution (an = 0-22 = < 33 = di2 = 0) which allows to compute the line-shape and saturation effects. A detailed description of the steady state solution for a three level system can be found in [35]. From those the appropriate equations for the intensity dependence of the excitation linewidth Avfwhm (FWHM full width at half maximum) and the fluorescence emission rate R for a single absorber can be easily derived [10] ... 

The frequency dependence of the gain coefficient a(v) is related to the line profile g(y — vq) of the amplifying transition. Without saturation effects (i.e., jfor small intensities), a(v) directly reflects this line shape, for homogeneous as well as for inhomogeneous profiles. According to (2.83) we obtain with the Einstein coefficienct Bik... 

Second, the ESR spectra of PVC heat-treated at <400 °C shows strong saturation phenomena in a vacuum. The effect of oxygen is purely physical and only shortens the spin-lattice relaxation time. In the chars heat-treated at >400 C, oxygen is chemisorbed on the char and decreases the line intensity. 

One effect of saturation, and the dependence of e on /, is to decrease the maximum absorption intensity of a spectral line. The central part of the line is flattened and the intensity of the wings is increased. The result is that the line is broadened, and the effect is known as power, or saturation, broadening. Typically, microwave power of the order of 1 mW cm may produce such broadening. Minimizing the power of the source and reducing the absorption path length t can limit the effects of power broadening. 

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