Gaussian line shape,

Two samples of the same phosphor crystal have quite different thicknesses, so that one of them has a peak optical density of 3 at a frequency of vo. while the other one has a peak optical density of 0.2 at vq. Assume a half width at half maximum of Av = IGHz and a peak wavelength of 600 nm, and draw the absorption spectra (optical density versus frequency) for both samples. Then show the absorbance and transmittance spectra that you expect to obtain for both samples and compare them with the corresponding absorption spectra. (To be more precise, you can suppose that both bands have a Lorentzian profile, and use expression (1.8), or a Gaussian line shape, and then use expression (1.9).)... 

A computer simulation was performed to observe the effect of variable line width on the calculated ESR first derivative spectrum. Since dipolar interaction is the major contribution to line broadening in the ESR spectrum of PVC radicals, a Gaussian line shape is expected for each of the ten absorptions. Therefore each line was assigned a Gaussian shape, the variables being relative amplitude position in the spectrum and line... 

To determine the excitation energy of the lowest electronic level the contributions in the absorption spectrum from transitions to different vibrational modes of the excited state have to be separated. In the deconvolution of the absorption spectra Gaussian line shapes are assumed for the transitions to the different vibrational levels. The analysis leads to the transition wavelength A00 for the excitation from the ground state to the zero vibrational level of the excited state. 

Therefore, the fractional column density (and the total column density N according to Eq. (20)) can only be obtained from the optical depth if Tex is known. If a gaussian line shape is assumed, integration of the observed line profile yields... 

Two examples of experimental UPS data and their comparison to VEH band calculations are given in Fig. 22a and b for trans-PA and PPV [197]. The DOS values calculated have been broadened by an arbitrary Gaussian line shape (the energy resolution of UPS is no more than a fraction of 1 eV) but not corrected for the energy dependence of the cross sections. They have been shifted in energy as discussed below. There is good overall agreement in the top 5 eV of the valence band, and the main features of the experimental spectrum correspond to calculated maxima of the DOS. 

The absorption and emission bands have gaussian line shapes with their peaks separated by 2fV, as is illustrated in Fig. 8.4. The difference in energy is known as the Stokes shift as the strength of the electron-phonon coupling increases, so do the Stokes shift and the line widths. 

The information of an EPR spectrum is contained in (i) the resonance frequency (in practice the g value), (ii) the line shape or spectral structure, and (iii) the relaxation behaviour. Comparison of the characteristic parameters with those of known species often leads to identification of the paramagnetic entity under investigation. More fundamentally, they give insight into the magnetic interactions to which the unpaired electron is subjected, and thus into the structure of its environment. In actuality, the stick spectrum of Fig. Ic will consist of resonances with Lorentzian line shape in the case of individual transitions as in Fig. 1, or with Gaussian line shape when many different unresolved hyperfine interactions are... 

Many spectral bands can be closely approximated by a Gaussian line shape when the independent variable v is in energy units, e.g., cm . The absorbance A at a wavenumber v is given by equation 21-1, where Amax is the band maximum, Vmax is the wavenumber of the band maximum and Av is the half-width. 

Figure 3. 29Si NMR spectra of Compol. Part a Direct polarization MAS, 300 accumulations, and repetition time of 400 s. Part b Deconvoluted spectrum using Gaussian line shape. Continued on next page.

The linewidth, or lineshape, is the third aspect of the ESR spectrum important in any study of radicals. The two most frequently encountered lineshapes observed are the Lorentzian and Gaussian. The Gaussian line-shape is observed when the line is the superposition of a large number of unresolved individual components, such a line being referred to as inho-mogeneously broadened. More important is the Lorentzian lineshape which is often observed for radicals in solution, when complications due to unresolved hyperfine splittings do not occur. The Lorentzian lineshape may be defined by... 

Figure 5. Top panel) UV absorption spectrum of CHFjCFjOj circles, Ref. 39. Bottom panel) UV absorption spectrum of CF3CFHO2 solid line, Ref. 92 circles. Ref. 52 triangles. Ref. 89. Dashed lines are fits of the spectra to the Gaussian line shape using the parameters listed in Table S.

---