Doppler distribution broadening

The second perturbation, namely the thermal motion of emitter nuclei, produce a Doppler-effect broadening of the emission line and causes it to extend in part beyond the energy Eq even though centered at Ey (= Eq—Er). The y-ray energy will be broadened into a distribution by the Doppler-effect energy, E = MvV, which is proportional to the initial velocity, Vx. from the random thermal motion of the atom, and v from the recoil of the nucleus. 

Doppler broadening arises from the random thermal agitation of the active systems, each of which, in its own test frame, sees the appHed light field at a different frequency. When averaged over a Maxwellian velocity distribution, ie, assuming noninteracting species in thermal equilibrium, this yields a line width (fwhm) in cm C... 

Doppler broadening arises from the random thermal motion of the atoms relative to the observer. The velocity V, of an atom in the line of sight will vary according to the Maxwell distribution, the atoms moving in all directions relative to the observer. The frequency will be displaced by... 

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. 

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. 

The positron-trap technique has been used by Surko and coworkers to measure the Doppler broadening of the 511 keV line for positrons in helium gas. This method does not have the drawback of the experiment described above, in which both positronium and free-positron events overlap on the angular distribution curves here the positrons are thermalized prior to the introduction of the gas and therefore cannot form positronium. A comparison of the theoretically predicted and experimentally measured Doppler spectra (Van Reeth et al., 1996) is shown in Figure 6.16. The theoretical results were obtained from the variational wave functions for low energy positron-helium scattering calculated by Van Reeth and Humberston (1995b) see equations (3.75) and (3.77). 

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. 

In a gas of atoms at finite temperature, the atoms move according to the Maxwell38-Boltzmann39 distribution of speeds, which collectively cause a Doppler broadening A/., /2,Soppier that is typically two orders of magnitude greater than the natural linewidth A/l1/2 ae... 

Dynamic light scattering (DLS), also called photon correlation spectroscopy (PCS) or laser light scattering (LLS) is a technique based on the principle that moving objects cause a frequency shift due to the Doppler effect. If a solution of macromolecules with random Brownian motion is illuminated with monochromatic laser light, the scattered light should contain a distribution of frequencies about the incident frequency the spectral line is virtually broadened. The width of the distribution is related to the MMD. 

In the field of positronium chemistry AMOC combines the positronlifetime analysis which is especially sensitive to detect long-lived ortho-positronium (o-Ps) with the Doppler-broadening-measurement technique which is particularly suitable for the observation of the para-positronium (p-Ps) state with its characteristic narrow momentum distribution. In addition,... 

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