Doppler broadening shift

There are well-exploited connections between experimental phenomena and electron momentum densities. Inelastic scattering [167,181-184] of high-energy electrons, X rays, or y rays by electrons in a molecule allows us to measure the electron momentum density of the molecule. The observable is the intensity of the Compton scattering at wavelengths shifted, by a Doppler broadening-like... 

Figure 1.1a shows the Gaussian function. The Lorentzian shape is similar to the Gaussian, but falls off more slowly. The Doppler shift of radiation from an emitting molecule is proportional to its velocity component in the direction of observation. The one-dimensional distribution of speeds in a gas is a Gaussian function. (See any physical-chemistry text.) Hence when Doppler broadening is dominant, we get a Gaussian-shaped line. 

In practice, the effect known as Doppler broadening is a much more severe limitation. This results from the motions of the atoms with respect to the observer, and produces a shift in the frequency v of a line according to the relative velocity v. 

In this section we introduce three techniques frequently encountered in positron physics, namely those used to measure annihilation lifetimes and the Doppler broadening (or Doppler shift) and angular correlation of the annihilation radiation. These techniques, or variants thereof, are encountered throughout the rest of this work, and here we briefly describe... 

The Doppler shift will vary from zero for zero scattering angle to maximum for back-scattering (0 = 180°). The width of the Doppler-broadened peak at half-height (Figure 3.9) is related to the diffusion coefficient by... 

In the case of the 1S-3S transition in hydrogen and for an estimated velocity of v=3km/s, the shift is Av =l4A kHz. We can t measure the velocity distribution by observing the Doppler broadened 1S-2P transition at 121 nm with a colinear laser beam, because the production of Lyman-a radiation is very difficult. In 1991 a method to compensate or at least to measure this effect was proposed by F. Biraben [7]. The basic idea is to apply a transverse magnetic field B in the atom-laser interaction region. This field has two effects ... 

Doppler shifts due to the low thermal velocities of the highly-charged ions in the EBIT are not significant sources of uncertainty. On average the Doppler shifts will be zero as there is no preferred direction of motion. Doppler broadening is 1.8 eV for IkeV ions and we allow for a possible 1% asymmetry of velocity distribution resulting in a maximum Doppler shift of < 0.02 eV or < 4 ppm. 

First order Doppler broadening can be eliminated by using a standing wave geometry (i.e. oppositely running waves) to excite the two-photon transition. The fractional second order Doppler shift, v1 c2, is less than 2 x 10-16 at a temperature of 1 mK. 

Figure 7.27 Doppler broadening spectrum from two detectors in coincidence as a function of the Doppler shift momentum in atomic units. MSSQ samples with 0% and 40% porogen are shown. The lead filter is used to stop the low energy third photon from reaching a detector. In that case, only two photon events are observed. Statistical errors are of the order of the line width and smaller.

In Ar and even more pronounced, in Kr and Xe, the lineshape functions 5 (t) show indeed a clear shift of the juvenile Doppler broadening to higher positron ages (Figure 14.8). 

High resolution studies by conventional spectroscopy are genuinely hampered by Doppler-broadening of the rotation-vibration lines in the low pressure regime. Individual Doppler-shifted frequencies contribute to the (normalized) Doppler-broadened line shape, due to the distribution of molecular velocities along the direction of observation... 

Two-photon spectroscopy may also be used to obtain highest-resolution spectra. Doppler broadening, which originates in the random motion of molecules in the gas phase, prevents individual rotational lines of a vibronic transition from being resolved in conventional spectroscopy. However, if two photons of extremely monochromatic light coming from exactly opposite directions are absorbed simultaneously, the Doppler shifts of the two photons just cancel each other and the Doppler broadening is eliminated. As... 

Doppler broadening results from frequency shift due to translational motion and has no relationship to molecular interaction. It also is negligible in comparison to widths treated in this paper. 

Doppler broadening is not an important factor in the lower MMW frequency region at ambient temperatures or below. At higher MMW frequencies its contribution to the overall linewidth could, however, become significant. Its effect can be readily demonstrated by recalling that the relative frequency shift in the spectral absorption due to the velocity of the molecule v with respect to the direction of the MMW radiation is ... 

The relatively high concentration of foreign molecules in flame AAS results in a Lorentzian broadening line value similar to that of the Doppler broadening value. The frequency shift may be considerable and lead to a... 

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