Line Profile of the Emitted Radiation

Because the amplitude x t) of the oscillation decreases gradually, the frequency of the emitted radiation is no longer monochromatic as it would be for an oscillation with constant amplitude. Instead, it shows a frequency distribution related to the function x(0 in (3.5) by a Fourier transformation (Fig. 3.2). 

The damped oscillation x t) can be described as a superposition of monochromatic oscillations exp(iu)r) with slightly different frequencies co and amplitudes A(o)) 

The lower integration limit is taken to be zero because x t) = 0 for t 0. Equation (3.7) can readily be integrated to give the complex amplitudes 

The real intensity /(m) oc A(co)A (co) contains terms with (co—coo) and (co -hcoo) in the denominator. In the vicinity of the central frequency coo of an atomic transition 

For comparison of different line profiles it is useful to define a normalized intensity profile L(co — coo) = I co — coq)/ Iq with /q = / 7 co)dco such that 

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In most laboratory sources the excitation temperature decreases towards the boundary of the discharge region. Consequently the absorption in this part of the source is increased and the profile of the emitted radiation is not only appreciably broadened but often shov/s a pronounced dip at the centre of the line. This effect is known as self reversal and it has been studied in detail by Cowan and Diecke (1948). It is particularly important that self reversal is avoided in the lamps used in the resonance fluorescence experiments described in Chapters 15-17, for the strengths of the signals are proportional to the intensity at the line centre frequency... 

It would appear that measurement of the integrated absorption coefficient should furnish an ideal method of quantitative analysis. In practice, however, the absolute measurement of the absorption coefficients of atomic spectral lines is extremely difficult. The natural line width of an atomic spectral line is about 10 5 nm, but owing to the influence of Doppler and pressure effects, the line is broadened to about 0.002 nm at flame temperatures of2000-3000 K. To measure the absorption coefficient of a line thus broadened would require a spectrometer with a resolving power of 500000. This difficulty was overcome by Walsh,41 who used a source of sharp emission lines with a much smaller half width than the absorption line, and the radiation frequency of which is centred on the absorption frequency. In this way, the absorption coefficient at the centre of the line, Kmax, may be measured. If the profile of the absorption line is assumed to be due only to Doppler broadening, then there is a relationship between Kmax and N0. Thus the only requirement of the spectrometer is that it shall be capable of isolating the required resonance line from all other lines emitted by the source. 

The radiation emitted in a radiation source is absorbed by ground state atoms of the same species. This phenomenon is known as self-absorption (for an explanation, see e.g., Ref. [15]). As the chance that an absorbed photon is re-emitted is < 1, this causes the observed radiation to be smaller than the emitted radiation. When Io is the intensity emitted at the wavelength of the line maximum and Pe (v) is the profile function, the intensity distribution for a line emitted by a radiation source over the profile of a line equals Io Pe (v) and the intensity observed after the radiation has passed through a layer with a number density of absorbing atoms of nA is ... 

Accordingly, it was very soon found that using sources for which the physical widths of the emitted analyte lines are low is more attractive. This is necessary so as to obtain high absorbances, as can be understood from Fig. 76. Indeed, when the bandwidth of the primary radiation is low with respect to the absorption profile of the line, a higher absorption results from a specific amount of analyte as compared with that for a broad primary signal. Primary radiation where narrow atomic lines are emitted is obtained with low-pressure discharges as realized in hollow cathode lamps or low-pressure rf discharges. Recently, however, the availability of narrow-band and tunable laser sources, such as the diode lasers, has opened up new per-... 

The light source. In these experiments the profile of the absorption line is studied under high resolution and the detector receives radiation contained within a very small wavelength or frequency interval. Moreover, the relatively small solid angle of the spectrometer allows only a small fraction of the light emitted by the source to be collected. Consequently a source of high intensity is required and in these experiments the continuum emission from... 

Studies of profiles of Ba ion lines in plasmas formed by an Nd YAG laser at 1064 nm on YBa,Cu,0, in air at atmospheric pressure as a function of laser power showed the line at 455.4 nm to be strongly self-reversed at all laser powers, and a third peak to evolve in the centre of the self-reversed profile at power densities above 16 GW/cm This third peak was ascribed to fluorescence of Ba ions that absorbed emitted radiation, the absorption peaking 120 ns after the initial laser pulse. 

A primary source is used which emits the element-specific radiation. Originally continuous sources were used and the primary radiation required was isolated with a high-resolution spectrometer. However, owing to the low radiant densities of these sources, detector noise limitations were encounterd or the spectral bandwidth was too large to obtain a sufficiently high sensitivity. Indeed, as the width of atomic spectral lines at atmospheric pressure is of the order of 2 pm, one would need for a spectral line with 7. = 400 nm a practical resolving power of 200 000 in order to obtain primary radiation that was as narrow as the absorption profile. This is absolutely necessary to realize the full sensitivity and power of detection of AAS. Therefore, it is generally more attractive to use a source which emits possibly only a few and usually narrow atomic spectral lines. Then low-cost monochromators can be used to isolate the radiation. 

AAS is based on measuring the absorbance of a spectral line by using a radiation source emitting a sharp line. Even the sharpest line that can be produced by a modern spectrometer has a finite width which is extremely important in applications of both AAS and AFS. The profile of a spectral line is presented in Figure 7. 

Self-absorption occurs when radiation emitted by the source is absorbed by atoms of the same species in the ground state. Since the probabiUty of re-emission of an absorbed photon is always smaller than unity, self absorption results in a reduction of the radiation produced. The intensity distribution of an emission line is IoPe(v), where Iq stands for the intensity emitted at the line maximum, and P (v) for the profile function. After passage through a layer of absorbing species with a number density of absorbing species, the intensity distribution is ... 

It is assumed that only the background absorption is measured at high lamp current (which is an only partially valid assumption), however, the broadening of the line profile is limited and self-reversal is not complete. Thus, radiation is still emitted at the centre of the emission line and is absorbed by the analyte, and will subsequently be subtracted from the gross absorption of the analyte. This significantly reduces the sensitivity of the determination, with an average loss of sensitivity of ca. 45 % being observed for the elements most commonly determined by... 

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