Gaussian doublet

A 90° Gaussian pulse is employed as an excitation pulse. In the case of a simple AX spin system, the delay t between the first, soft 90° excitation pulse and the final, hard 90° detection pulse is adjusted to correspond to the coupling constant JJ x (Fig- 7.2). If the excitation frequency corresponds to the chemical shift frequency of nucleus A, then the doublet of nucleus A will disappear and the total transfer of magnetization to nucleus X will produce an antiphase doublet (Fig. 7.3). The antiphase structure of the multiplets can be removed by employing a refocused ID COSY experiment (Hore, 1983). 

The Na I D-lines have wavelengths and oscillator strengths A,i = 5896 A, /i = 1 /3, and X2 = 5889 A, f2 — 2/3. In a certain interstellar cloud, their equivalent widths are measured to be 230 mA and 370 mA respectively, with a maximum error of 30 mA in each case. Assuming a single cloud with a Gaussian velocity dispersion, use the exponential curve of growth to find preferred values of Na I column density and b, and approximate error limits for each of these two parameters. (Doublet ratio method.)... 

Figure 6.37. XPS S2p line (black dots) measured ex situ at RT for a TTF[Ni(dmit)2]2 thin film. Also shown is a least-squares fit (Gaussians), after a Shirley-type background subtraction, where each line (dashed) is composed of a spin-orbit split doublet (compare to Fig. 1.31). The addition of the three lines results in the continuous grey line. Reprinted with permission from de Caro et al., 2004.

The method used to calculate the "best" 2-theta for each reflection from step-scan data was developed especially for this system. Each peak is actually a doublet—one peak due to 04 radiation and another due to a2 radiation. The method assumes that this doublet may be fit by the sum of two Gaussian curves separated by A20 which can be calculated from the wavelengths and the approximate 2-theta of the 04 peak ... 

Mossbauer spectrometry is a powerful means for the elucidation of the state of iron in materials [44,138-142,145]. Figure 4.63 [44] shows the 57Fe Mossbauer spectra of the natural zeolite rocks, such as MP, C2, Cl, and C4 (see Table 4.1). In Table 4.12, the Mossbauer parameters calculated with the help of the numerical resolution of the spectra presented in Figure 4.63 are reported. That is, with the help of the recorded spectra, the accurate peak positions, integrated intensities, as well as the FWHM of each peak were calculated. This calculation was carried out by fitting the spectra with three quadrupole doublets one for site 1, another for site 2, and a last one for site 3 [44], The peaks were simulated with Gaussian functions and the fitting process for the numerical resolution of the spectra was carried was carried out with a peak separation and analysis software, developed for this purpose [44,145] based on a least square procedure [48],... 

The low-temperature spectrum of PPyFeEDTA (Figure 12.27(b)) exhibits pronounced magnetic splitting with a well-defined sextet. The spectrum also shows a broad absorption due to unresolved magnetic structure (which has been fitted to a Gaussian) and a central region for which several fitting combinations were tried. The preferred fit shown uses three doublets, but the parameters should be treated with caution. The... 

This view is borne out by the spectroscopic study of Allen and Warren (103). For a high-spin d system the ground state is a Aij level, and all d—d transitions would be spin-forbidden, but the intensities of the bands observed below about 25 kK. are comparable with those found for the spin-allowed bands of low-spin NiFe . Whilst it is not possible to place too much rehance on intensity values obtained by reflectance (s. Sect. 1 (iv)), it is usually easy to distinguish between spin-allowed and spin-forbidden transitions, and on this basis the bands lying between 17 and 25 kK.. (Table 3 (iv)) are assigned as spin-allowed doublet-doublet excitations, whilst the much weaker absorptions at 6.4 and 10.3 AK. represent transitions to quartet states. Resolution of the absorption r on above 15 kK., by Gaussian analysis, yields the peak positions shoAvn in the Table, and the bands may be fitted by the parameters Dy=2030 cm. i. 

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