Lorentzian term

Fig. 2. (a) Raw 300 MHz proton spectrum of a mixture of acetone and ethanol in deuteri-ochloroform (b) after reference deconvolution using the acetone signal as reference and an ideal lineshape of a 1 Hz wide Lorentzian and (c) after reference deconvolution with an ideal lineshape characterized by a negative Lorentzian width of 0.1 Hz and a Gaussian width of 0.4 Hz. The 0.1 Hz Lorentzian term represents the approximate difference in natural linewidth between the ethanol and acetone signals, and is responsible for the wings on... 

A more refined parameterization allows for the several Lorentzian terms in equations similar to Equations (1.138) and (1.140) [5,6,16]. They contain a number of correlation parameters A or At(i = 1,2,...) the interrelations between parameters A and A depend on this number. 

The function 7obs (r) can easily be evaluated for any value of v. Further, the analytical properties may be considered. Obviously, the asymptotic value of /oi)a(i ) for Smax - -oo is the true spectrum I v). On the other hand, if the widths of the Lorentzian terms are reduced drastically, we obtain... 

The spectral density function, J(co0), is modeled as a constant, a, plus a sum of Lorentzian terms, each characterized by an amplitude parameter, / , and a correlation time, rc ... 

In order to obtain a more realistic description of reorientational motion of intemuclear axes in real molecules in solution, many improvements of the tcf of equation Bl.13.11 have been proposed [6]. Some of these models are characterized in table Bl.13.1. The entry number of terms refers to the number of exponential functions in the relevant tcf or, correspondingly, the number of Lorentzian terms in the spectral density function. 

Obviously, the treatment of the experimentally observed noise component as Lorentizian is also nothing more than an approximation, since in the case of several kinetic states, which we assumed in the interpretation of the H-H equations discussed above, there must be several Lorentzian terms in the integral spectrum. It is hence clear that the measurement precision available at present does not allow us to distinguish between these variants of ionic channel models. Nevertheless, it has already been possible to estimate the conductance of single K and Na" channels (several pmho) using noise measurement techniques, although the results reported by different authors are largely at variance. 

The quantity F from Equation 67 differs from that in Equation 2.3-56 owing to the appearance of a contribution of diffusion and to the mutual influence of diffusion and heat flux. Equation 66 does not comprise negligible non-Lorentzian terms like those in Ekjuation 2.3-3. 

In some cases, e.g. in " Np, the resonance lineshape contains in addition tto"the Lorentzian term of eq. (11) a weak dispersion term which has to be taken into account in precise data analysis (Goldwire and Hannon 1977). The situation in " Np is discussed by Asch et al. (1978). Due to the sharpness of F the velocities needed to destroy resonance absorption are quite small, usually in the range of 10 to lOOmm/s. The actual construction of Mossbauer spectrometers will be reviewed briefly in section 3.1. 

From a double minimum potential containing qiradratic, quartic, and Lorentzian terms defined by observed vibrational stmcture. Potential maximum 6809 cm [4]. For alternative potentials see also [5]. 

If now the detector is gated to receive fluorescence only for t > T, the Lorentzian term in the Fourier transform of (14.53) becomes... 

Molecular dynamics characterisations in solids can be carried out selectively using dipolar-dephasing experiments. Aliev and Courtier-Murias have shown that the introduction of a sum of Lorentzian and Gaussian functions greatly improve fittings of the intensity versus time data for protonated carbons in dipolar-dephasing experiments. The Lorentzian term accounts for remote intra- and intermolecular dipole-dipole... 

AaQL/2) /(I + X ). Since AaQL l, the selection of the uncrossing angle 0 allows one to make either the dispersion term (larger 0) or the Lorentzian term (0=0) dominant. 

Contrary to the situation in polarization spectroscopy, where for slightly uncrossed polarizers the line shape of the polarization signal is a superposition of Lorentzian and dispersion profiles, here a pure dispevsum line profile can be obtained without distortion by a Lorentzian term. To achieve this, the output of the lock-in amplifier that controls the phase is fed into another lock-in, tuned to a frequency f2 (f2 i) which the saturating pump beam is chopped. The output of the first lock-in is always proportional to (o)) since it drives the servo loop to bring (w) back to zero. 

Rotational motion or other localised motions give rise to an unbroadened elastic component and a broadened quasi-elastic component that may be comprised of sev l Lorentzian terms. The width of the broadened term is inversely related to the characteristic time of the motion. The ratio of elastic to elastic plus quasi-elastic intensity varies with Q and is determined by the geometry of the motion. This ratio... 

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