Doppler lineshapes

Figure C3.3.3. A schematic drawing of tlie Doppler-lineshape profile for a typical infrared transition in a small...

Radiative Processes.—A large number of papers concerned with the various aspects of the electronic absorption and emission processes in atomic species have appeared. Of general interest is a paper which presents an expression suitable for the evaluation of the infinite sum describing absorption due to a hydrogenic series of Lorenzian lines.444 The Doppler lineshape in atomic transitions,448 collision effects on lineshapes of atomic transitions,44 the effect of metastable dimers on the radiative transition in pairs of atoms 447 and in donor-acceptor pairs,448 and other aspects of excitation transfer in two-atom systems,449- 480... 

For all of the eases eonsidered earlier, a C(t) funetion is subjeeted to Fourier transformation to obtain a speetral lineshape funetion I(co), whieh then provides the essential ingredient for eomputing the net rate of photon absorption. In this Fourier transform proeess, the variable co is assumed to be the frequeney of the eleetromagnetie field experienced by the molecules. The above considerations of Doppler shifting then leads one to realize that the correct functional form to use in converting C(t) to I(co) is ... 

An application for multiplexed diode-laser sensors with a potentially large impact is for measurements of important parameters at several locations in a gas turbine combustion system. In this example, illustrated schematically in Fig. 24.1, the multiplexed diode lasers are applied for simultaneous absorption measurements in the inlet, combustion, afterburner, and exhaust regions. For example, measurements of O2 mass flux at the inlet may be determined at the inlet from Doppler-shifted O2 absorption lineshapes near 760 nm. Measurements of gas temperature and H2O concentrations in the combustion and afterburner regions may be determined from H2O lineshape measurements near 1.4 pm. Finally, measurements of velocity, temperature, and species concentrations (e.g., CO, CO2, unburned hydrocarbons) may be recorded in the exhaust for the determination of momentum flux (component of thrust) and combustor emissions. 

To observe a 7s — 9 transition requires that there be a 9p admixture in the 9 state. For odd this admixture is provided by the diamagnetic interaction alone, which couples states of and 2, as described in Chapter 9. For even states the diamagnetic coupling spreads the 9p state to all the odd 9( states and the motional Stark effect mixes states of even and odd (. Due to the random velocities of the He atoms, the motional Stark effect and the Doppler effect also broaden the transitions. Together these two effects produce asymmetric lines for the transitions to the odd 9t states, and double peaked lines for the transitions to even 9( states. The difference between the lineshapes of transitions to the even and odd 9i states comes from the fact that the motional Stark shift enters the transitions to the odd 9( states once, in the frequency shift. However, it enters the transitions to the even 9( states twice, once in the frequency shift and once in the transition matrix element. Although peculiar, the line shapes of the observed transitions can be analyzed well enough to determine the energies of the 9( states of >2 quite accurately.25... 

The lineshape function g(V-Vc) is defined assuming a Voigt profile ( 7) which allows for a combination of Doppler and collision... 

At low density (< 1012 cm-3) and temperatures > 100 /jK the two-photon lineshape is a double exponential, exp(- p /<5p0) [3], as expected for Doppler-free two-photon excitation by a Gaussian laser beam of a thermal gas [29]. Here v is the laser detuning from resonance and 8v0 is the linewidth due to the finite interaction time of the atom with the laser beam. At low temperature, lines as narrow as 3 kHz (FWHM at 243 nm) have been observed. A detailed discussion of this lineshape in the trap and the appearance of sidebands due to coherence effects for repeated crossing of the laser beam can be found in [30]. 

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... 

For the moment we shall consider the standard method for describing the Doppler-broadened linewidth—i.e. by using a simple lineshape parameter. By far the most common parameters used—called S and W—are defined... 

Figure 8.4 Doppler broadening lineshape parameter vs temperature in DyBa2Cu307 Yo.5Pro.5Ba2Cu307 and PrBa2Cu307. The arrow indicates Tc, From Jung et al [34,35].

Figure 8.9 Variation with quenching temperature of, (a) positron lifetime, (b) Doppler broadened lineshape parameter, I, and (c) oxygen deficiency, as obtained from weight loss (+) and Tc (o) measurements. From Bharathi et al. [54].

The linewidth of annihilation from the free-positron state is Doppler-broadening measurements. In lifetime measurements the PsF component hides beneath the o-Ps component which has a similar lifetime. This is a case where the two-dimensional data analysis shows its great advantage As the Doppler broadening of each positron state is determined in its own time regime even positron states with similar features may be seperated from each other. Moreover, a tentative fitting procedure with only the three positron states as in pure water did not come to a satisfactory result with the AMOC histogram of the NaF solution. 

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). 

Here C is a lineshape factor whose value depends on whether the transition is Doppler- or pressure-broadened. 

Figure 1.13 Velocity Modulation Spectra (VMS). An AC electric field applied along the laser propagation direction causes the velocity, hence the Doppler shift, of ionic but not neutral species to be modulated. Spectrum (a) shows 127 MHz = 0.0042 cm-1 Doppler shifts of a 2479.4113 cm-1 ArH+ transition. Also shown is an Ar line that does not exhibit an electric field dependent Doppler shift. This spectrum was actually recorded at a fixed (DC) electric field using counter-propagating (frequency modulated) laser beams (from Haese, et ai, 1983). Spectrum (b) shows a portion of the VMS Nj A2 Hu — X2E (7,3) band. Since the AC electric field causes the Nj line to be frequency modulated, phase sensitive detection at the modulation frequency (If) results in a first derivative lineshape. Spectra (b) and (c) were recorded simultaneously. The Nj lines are absent from spectrum (c), which was recorded in population modulation mode by phase sensitive detection at twice the modulation frequency (2f). Spectrum (c) contains a few lines belonging to a N2 B3I19 — A3eJ First Positive baud. The population of N2 A3Ej is modulated at 2f because each half cycle of the AC field results in a full cycle modulation of the population of electronically excited N2 molecules. (Spectra (b) and (c) axe from Radunsky and Saykally, 1987.)...

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