Linewidth, Doppler-broadened

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... 

This fluorescence is emitted into all modes of the EM field within the spectral width of the fluorescence line. According to Example 2.1 in Sect. 2.1, there are about 3 x 10 modes/cm within the Doppler-broadened linewidth Ayo = 10 Hz at A = 500 nm. The mean number of fluorescence photons per mode is therefore small. 

Natural linewidths are broadened by several mechanisms. Those effective in the gas phase include collisional and Doppler broadening. Collisional broadening results when an optically active system experiences perturbations by other species. Collisions effectively reduce the natural lifetime, so the broadening depends on a characteristic impact time, that is typically 1 ps at atmospheric pressure ... 

Linewidth The spread in wavelengths or frequencies associated with a transition in an atom or molecule. There are three contributions natural linewidth associated with the lifetime of the transition pressure broadening associated with the presence with the other molecules nearby Doppler broadening associated with relative motion of the molecule and light source. 

Usually, mainly Doppler broadening determines the gain profile of a particular laser transition. Indeed, due to the different configurations achievable with gas lasers (namely, a large cavity length), the laser line can be narrower than the Doppler linewidth. Different experimental realizations of single-mode lasers are detailed elsewhere (Demtroder, 2(X)3). 

Figure 21-17 Relative bandwidths of hollow-cathode emission, atomic absorption, and a monochromator. Linewidths are measured at half the signal height. The linewidth from the hollow cathode is relatively narrow because the gas temperature in the lamp is lower than a flame temperature (so there is less Doppler broadening) and the pressure in the lamp is lower than the pressure in a flame (so there is less pressure broadening).

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... 

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. 

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 ... 

Once the sample pressure has become sufficiently high that Doppler broadening may be neglected, the peak signal from an unsaturated spectral line becomes independent of the pressure for a particular sample composition (Section 1.2). In this regime Omax depends on frequency, temperature, linewidth and the molecular concentration of the state under study. As an isotopomer, stereoisomer or vibrational excimer, the species concentration will be less than that of its parent. 

MMW spectra possess a number of features that make direct readout of sample concentration from a measurement less than straightforward. Although the peak absorption coefficient of the sample may be determined in several ways itemised below. Equations 1.24 and 1.48 show that additional information about linewidth, temperature, occupation of vibrational states and even Doppler broadening is required to obtain the analyte concentration. Such calculations can be incorporated into any anal5dic program, but the parameters required are often not readily available in the literature and may need to be determined directly. 

The half width of elemental lines is of the order of 0.002 nm when observed by emission spectroscopy with flame or electrothermal atomisation. A number of reasons can cause broadening of the linewidth, of which the most important and best understood are natural, pressure, resonance, and Doppler broadening. If a stable and sensitive detection is to be achieved, the linewidth of the excitation radiation must be narrower than the full width at half maximum (FWHM) of the analyte line. Under these conditions, the entire radiant energy produced by the excitation source will be available for absorption by the analyte. The typical line sources used for atomic absorption are element specific excitation sources such as the hollow cathode lamp or the electrodeless discharge lamp. But even continuum sources can be used with appropriate instrumental designs. 

Values for AXj) are low for heavy elements (e.g. Au(II) at 200.08 nm has a value of 0.8 pm, whereas AXj) values are high for light elements such as Be(II) at 313.11 nm that has a value of 5.9 pm. Collisional broadening results due to collisions among analyte ions, atoms, and neutral Ar atoms and has also been called pressure broadening. Doppler broadening is dominant near the center of the band, whereas collision broadening dominates near the tails. AE linewidths dictate what resolution is needed to resolve one AE emission line from another. For each transition metal, there is a plethora of lines to consider. 

D13.1 (1) Doppler broadening. This contribution to the linewidth is due to the E)oppler effect, which shifts the... 

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