Absorptive lineshape

Lee S-Y 1998 Forward and inverse transforms between the absorption lineshape and Raman excitation profiles XVith int. Conf on Raman Spectroscopy ed A M Heyns (New York Wiley) pp 48-51... 

The Time Dependent Processes Seetion uses time-dependent perturbation theory, eombined with the elassieal eleetrie and magnetie fields that arise due to the interaetion of photons with the nuelei and eleetrons of a moleeule, to derive expressions for the rates of transitions among atomie or moleeular eleetronie, vibrational, and rotational states indueed by photon absorption or emission. Sourees of line broadening and time eorrelation funetion treatments of absorption lineshapes are briefly introdueed. Finally, transitions indueed by eollisions rather than by eleetromagnetie fields are briefly treated to provide an introduetion to the subjeet of theoretieal ehemieal dynamies. 

An application for multiplexed diode-laser sensors with a potentially large impact is for measurements of important parameters at several locations in a gas turbine combustion system. In this example, illustrated schematically in Fig. 24.1, the multiplexed diode lasers are applied for simultaneous absorption measurements in the inlet, combustion, afterburner, and exhaust regions. For example, measurements of O2 mass flux at the inlet may be determined at the inlet from Doppler-shifted O2 absorption lineshapes near 760 nm. Measurements of gas temperature and H2O concentrations in the combustion and afterburner regions may be determined from H2O lineshape measurements near 1.4 pm. Finally, measurements of velocity, temperature, and species concentrations (e.g., CO, CO2, unburned hydrocarbons) may be recorded in the exhaust for the determination of momentum flux (component of thrust) and combustor emissions. 

The double quantum filter eliminates or at least suppresses the strong signals from protons that do not experience J-coupling, e.g. the solvent signal, which would otherwise dominate the spectrum and possibly be a source of troublesome tl noise. Compared to a phase-sensitive but non-DQ-filtered COSY with pure absorption lineshapes for the cross peaks but mixed lineshapes for the diagonal peaks, the phase-sensitive, DQ-filtered COSY has pure absoiption lineshapes throughout. 

The basic processing of ID and 2D data requires obligatory processing steps for transforming the raw data (FID) into a "readable spectrum, i.e. Fourier transformation and phase correction to produce a spectrum with absorptive lineshapes. Finally, a few additional step.s (calibration, peak picking, integration) as discussed in chapter 4 are required before the spectrum is eventually plotted. 

Figure 1. Calculated absorption lineshapes and representative C-13 spectra for polycrystalline samples (a) an axially symmetric chemical shielding tensor (o. and

Here T2 is transverse relaxation time of an electron spin. The EPR absorption lineshape is related to free induction decay G(t) through the Fourier transformation [16]. After averaging over all angles between the surface and the external magnetic field H the following equation was obtained for D = 2 systems [138] ... 

The Fourier transform converts the FID into a Lorentzian peak with absorptive lineshape (after phase correction). The full width of this peak at one half of the peak s height (the linewidth ) is inversely related to the decay time constant of the FID, ... 

Kramers-Kronig (KK) transformation of the reflection spectra. This provides the optical absorption "(cu) semiexperimentally and allows a thorough analysis of the various relaxation mechanisms creating the absorption lineshape (2.102), (2.111) of an ideal finite crystal in its phonon bath. This method is currently used. However, two major difficulties often obscure the credibility of the results ... 

In die Fourier transform of a real time series, die peakshapes in the real and imaginary halves of die spectrum differ. Ideally, the real spectrum corresponds to an absorption lineshape, and die imaginary spectrum to a dispersion lineshape, as illustrated in Figure 3.20. The absorption lineshape is equivalent to a pure peakshape such as a Lorentzian or Gaussian, whereas die dispersion lineshape is a little like a derivative. 

Both Langhoff and Robinson 58> and Delory and Trie 59> have considered the effects on the emission decay curves and on the absorption lineshapes of variations with energy in the density of states and in the coupling strengths of the dense manifold with the intensity-carrying discrete state. The former workers also extended their treatment to include coupling with a second manifold, the radiation field continuum. 

For both NMR spectroscopy in the solid state and EPR spectroscopy in the liquid state it is possible to determine a fairly large number of parameters s . After solving this first problem, one has then to determine the absorption lineshapes in terms of this information. The main aim of this chapter is to show the algorithm of Chapter III at work. However, before launching into this illustration, we would like to mention the alternative approaches currently being used in the field of magnetic resonance. 

We would also like to mention the informational approach, which determines the most probable absorption lineshapes given a limited amount of information, that is, a finite number of spectral moments. The method is based on minimizing the informational entropy. ... 

Figure 6. Absorption lineshape for a molecule in a triplet spin state dissolved in a disordered liquid. t>o 0. Frequency sweeps from Uy — - (i -I- 6) to oy = (i -t- 8). — 10 t)...

Figure 10. Absorption lineshape for an axial g-splitting interaction for a spin 1/2 system in the presence of an orienting potential. Vertical scales are expressed in the same units. Uq 0. (a) 10 i, (b) Dj 5xl0 ii. The frequency sweep ranges from - -fij to -...

Figure 11. Absorption lineshape for a molecule in a triplet spin state subjected to an orienting potential. Ug = 0. D — 10 t. The frequency sweep ranges from u,- — (i) -f S) to ay...

Figure 14. Absorption lineshape for a nitroxide radical dissolved in an ordered liquid. Magnetic parameters are the same as in Fig. 1. Hq — 3300 G. (a) = 0.3, (b) P2 0.6, (c)...

Longitudinal to zero-quantum transfer. A transfer of the type UyS - I Sy) gives rise to in-phase absorption lineshapes in w, and antiphase dispersion lineshapes in Wj. 

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