Lorentz broadening

Both lines are broadened independently and solely by adiabatic phase shift as in Lorentz and Weisskopf theories. They are Lorentzians of width (1 — cosa) and frequency shift (sin a). In general off-diagonal elements of f are not zero though they are less than diagonal elements. Consequently, the spectrum may collapse even in the adiabatic case when A 1/tc. However, adiabatic collapse is hardly ever achieved in the gas phase where l/rc > l/t0 > jS since A > 1/tc > j8 and hence only the resolved doublet limit is available. 

Thus the random phase gives rise to a Lorentz broadening of the spectral line. 

Blickensderfer et al. (119) have recently extended the Samson theory to include various vessel geometries under conditions of pure Doppler, pure Lorentz, and Voigt (a combination of Doppler, Lorentz, and natural broadening) line profiles. The quenching cross section can be obtained also by a dynamic method in which the decay of the fluorescence intensity is measured after the exciting light is cut off. If the initial fluorescence intensity is / and the intensity after a lime f is If, we obtain... 

It has been shown [Mitchell and Zemansky (21), p. 197] that the quenching of the Hg 2537 A line by foreign gases follows the Stern-Volmcr formula only when (1) Lorentz broadening [sec Section 1-6.1] by foreign gases is... 

For Doppler lines there is little broadening with increasing self-absorption whereas for lint s with a Lorentz distribution of frequencies, self-absorption leads to a marked broadening, especially at the wings of the line. 

There are other factors affecting the intensity of the peaks on a x-ray diffraction profile of a powdered sample. We have analyzed the structure factor, the polarization factor, and the broadening of the lines because of the dimensions of the crystallites. Now, we will analyze the multiplicity factor, the Lorentz factor, the absorption factor, the temperature factor, and the texture factor [21,22,24,26],... 

The factors that are included when calculating the intensity of a powder diffraction peak in a Bragg-Brentano geometry for a pure sample, composed of three-dimensional crystallites with a parallelepiped form, are the structure factor Fhkl 2=l/ TS )l2, the multiplicity factor, mm, the Lorentz polarization factor, LP(0), the absorption factor, A, the temperature factor, D(0), and the particle-size broadening factor, Bp(0). Then, the line intensity of a powder x-ray diffraction pattern is given by [20-22,24-26]... 

For purposes of display, the intensity of each calculated reflection was assumed to be distributed about its mean position according to Gaussian distributions in 20 and p. The breadths of these distributions represent the expected peak broadening due to finite crystallite sizes, the crystal mosaic, and paracrystal distortions, which are not available a priori from the model calculations. Additionally, we require an estimate for p1/2 for the Lorentz correction of meridional reflection intensities. The peak broadening distributions were selected of the form... 

This is collision between atoms of the same element in the ground state and results in an intensity distribution similar to Lorentz broadening but without line asymmetry or shift. The effect depends on concentration and half-widths which are very small and negligible when compared with other collisions. 

Spend time on the measurement of the WAXS intensity curve. If noise can be detected by the eye, data are insufficient for further analysis. Correct the raw data for varying absorption as a function of scattering angle depending on the geometry of the beamline setup (Sect. 7.6, p. 76). Measure and eliminate instrumental broadening (cf. Sect. 8.2.5.3). Carry out polarization correction, i.e., divide each intensity by the polarization factor (cf. Sect. 2.2.2 and ( [6], p. 99)). Transform the data to scattering vector representation (20 —> s). Carry out the Lorentz correction ... 

In fact, it is necessary to take into account the finite life time of the inner hole and the spectrum is the convolution product of the outer electronic distribution and the Lorentz distribution of the inner atomic level (7). As a consequence, the resolution depends on two factors one is the instrumental broadening the other is intrinsic and is due to the width of the inner level. 

The perturbational effects have been variously described as interruption broadening, resonance broadening, and statistical broadening. The perturbational line shape derived by Michelson was not correct even for pure interruption broadening because he neglected to average over all times between collisions. To do so results in the simplified Lorentz model. ... 

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