Absorption Lorentzian broadened

In the framework of the impact approximation of pressure broadening, the shape of an ordinary, allowed line is a Lorentzian. At low gas densities the profile would be sharp. With increasing pressure, the peak decreases linearly with density and the Lorentzian broadens in such a way that the area under the curve remains constant. This is more or less what we see in Fig. 3.36 at low enough density. Above a certain density, the l i(0) line shows an anomalous dispersion shape and finally turns upside down. The asymmetry of the profile increases with increasing density [258, 264, 345]. Besides the Ri(j) lines, we see of course also a purely collision-induced background, which arises from the other induced dipole components which do not interfere with the allowed lines its intensity varies as density squared in the low-density limit. In the Qi(j) lines, the intercollisional dip of absorption is clearly seen at low densities, it may be thought to arise from three-body collisional processes. The spectral moments and the integrated absorption coefficient thus show terms of a linear, quadratic and cubic density dependence,... 

For the purpose of comparison with the measured absorption coefficient, the theoretical spectra are convoluted with a Lorentzian broadening function F(E). This function is the sum of two terms. The first takes account of the core hole width and the second term is the width of the excited band energy, which is a function dependent on the mean free path of the excited electrons, and takes account of the photoelectron inelastic scattering which is energy dependent and varies for each material as shown in Fig. 1. Note that in this theory any broadening effect due to the experimental resolution and many-body effects, such as the influence of the core hole on the band states, are not included. 

Figure 10.13 The absorption spectrum of chlorophyll a/fMeOH) in MeOH (CPCM) in a 250-700 nm energy range as dissected into the contributions of the single transitions in all cases, Lorentzian broadening with FWHM of 500cm" have been applied. The experimental data obtained in a methanol solvent [318, 319] is also shown for comparison. For the most relevant (bands Q and B)...

Fig. 1. Error bounds for the nuclear resonance line shape of crystalline CaF2, broadened by a Lorentzian slit function (i.e., the energy absorption by the coupled nuclear spins, due to an exponentially damped harmonic perturbation by a radiofrequency magnetic field).

Broadening effects, other than from g- or hyperfine-anisotropies, generally lead to symmetrical absorption curves that are Gaussian or Lorentzian depending upon the broadening mechanism. 

For a Voigt function that is almost Lorentzian, the extent of Gaussian broadening can be visualized by plotting the dispersion of the lineshape, D f) against the absorption, A(f).76,77 For a pure Lorentzian lineshape, a circle is obtained. Hence, the extent of the departure from this circular shape indicates the extent of the Gaussian broadening. 

InSe and GaSe crystals are characterized with a weak interaction of 3D Wannier excitons with homopolar optical A -phonons [18, 19]. Therefore, when calculating the exciton absorption spectra, we took into consideration effects of broadening the exciton states using the standard convolution procedure (see in [18]) for theoretical values of a(7jco) the absorption coefficient in the Elliott s model [20] with y /io>) — 77 [n(E 2+/ 2)] the Lorentzian function in the Toyozawa s model [21], where r is the half-width at half-maximum which is usually associated with the lifetime tl/2r. 

A high-resolution spectrum of the clock transition is shown in Fig. 2. The clock-laser power was reduced to 30 nW to avoid saturation broadening. The fit with a lorentzian curve results in a linewidth of 170 Hz (FWHM), corresponding to a fractional resolution bv/v of 1.3 10-13. A spectral window of 200 Hz width contains 50% of all excitations. According to our present experimental control of the ion temperature, electromagnetic fields and vacuum conditions, no significant Doppler, Zeeman, Stark or collisional broadening of the absorption spectrum of the ion is expected beyond the level of 1 Hz. The linewidth is determined by the frequency instability of the laser and the lineshape is not exactly lorentzian... 

Investigation of methanol-pyridine complexes, on the other hand, produced a relatively narrow (75 cm 1 FWHM) bleached hole that is burned into the 260 cm 1 FWHM OH-stretch (v = 0 -> 1) absorption band. The methanofpyridinc complex OH-stretch absorption band was better fit by a Gaussian function than with a Lorentzian bandshape, indicating this system is inhomogeneously broadened on the >1 ps timescale. 

For the (SisOie) " cluster in C2 symmetry, the LUMO allowed for the L2,s absorption is 54a. Therefore, (2p) (54a) and (2p) °(54a) configurations were used for the transition state and final state calculations. In this case, the spectra were broadened by a Lorentzian of 1.0 eV (FWHM) taking into account the widths of observed peaks. The Si-(3s -I- 3d) PDOS and the Si L2,3-edge PACS are shown in Fig. 7 and Fig. 8. It is found that the PDOS is also a good approximation of the theoretical PACS in Si02. 

In indirect methods, the resonance parameters are determined from the energy dependence of the absorption spectrum. An important extra step — the non-linear fit of (t E) to a Lorentzian line shape — is required, in addition to the extensive dynamical calculations. The procedure is flawless for isolated resonances, especially if the harmonic inversion algorithms are employed, but the uncertainty of the fit grows as the resonances broaden, start to overlap and melt into the unresolved spectral background. The unimolecular dissociations of most molecules with a deep potential well feature overlapping resonances [133]. It is desirable, therefore, to have robust computational approaches which yield resonance parameters and wave functions without an intermediate fitting procedure, irrespective of whether the resonances are narrow or broad, overlapped or isolated. 

In general, and for the nonlinear hyperpolarizabilities to be derived below, one introduces r, for the transition between states w) and ). In effect the imaginary term iT o/2 takes the place of ie in Eq. (42). The linear absorption spectrum, which corresponds to the imaginary part of Eq. (45), will be built from smeared out Dirac delta functions of Lorentzian shape, i.e. the frequency-integrated absorption will remain constant regardless of the value of the lifetime broadening. The real part of the polarizability is related to the refractive index n of the sample... 

If the process is symmetrical (xf = Xb), then the relaxation time in each direction is equal to x/2. In writing equation (7.9.13) it is assumed that the absorption peaks have a Lorentzian shape. In addition, the line-broadening effects illustrated in fig. 7.18 are those for a symmetrical process. 

There are some further steps, which should also be included, and are quite straightforward in practice. The true profiles of the absorption lines are not Lorentzian, as assumed in the simple theory above, but are broadened by the Maxwellian velocity distribution ... 

The conducting phase of TMQ /16/. Microwave conductivity experiments, performed at low temperature on the samples used for the pressure experiment, have succeeded in showing an increase by a factor 10 from 300 K down to loo K, /41/. The possibility of susceptibility measurement via low field method is limited by the EPR line broadening occurring at low temperature and under pressure. The spin susceptibility was derived from a fit of the EPR absorption line shape with a Lorentzian curve. The proton relaxation time was measured under pressure at low field lOe- with a pulse spectrometer. Figures... 

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