Resonance, absorption practical width

It is a matter of historical interest that Mossbauer spectroscopy has its deepest root in the 129.4 keV transition line of lr, for which R.L. Mossbauer established recoilless nuclear resonance absorption for the first time while he was working on his thesis under Prof. Maier-Leibnitz at Heidelberg [267]. But this nuclear transition is, by far, not the easiest one among the four iridium Mossbauer transitions to use for solid-state applications the 129 keV excited state is rather short-lived (fi/2 = 90 ps) and consequently the line width is very broad. The 73 keV transition line of lr with the lowest transition energy and the narrowest natural line width (0.60 mm s ) fulfills best the practical requirements and therefore is, of all four iridium transitions, most often (in about 90% of all reports published on Ir Mossbauer spectroscopy) used in studying electronic stractures, bond properties, and magnetism. 

The recoilless nuclear resonance absorption of y-radiation (Mossbauer effect) has been verified for more than 40 elements, but only some 15 of them are suitable for practical applications [33, 34]. The limiting factors are the lifetime and the energy of the nuclear excited state involved in the Mossbauer transition. The lifetime determines the spectral line width, which should not exceed the hyperfine interaction energies to be observed. The transition energy of the y-quanta determines the recoil energy and thus the resonance effect [34]. 57Fe is by far the most suited and thus the most widely studied Mossbauer-active nuclide, and 57Fe Mossbauer spectroscopy has become a standard technique for the characterisation of SCO compounds of iron. 

A film of metal evaporated onto a glass microscope slide dramatically increases the internal reflectance at angles below the critical angle for to internal reflectance, 0., and causes some loss in the total internal reflection (TIR) region. For monochromatic light incident on a metal film roughly 50 nm thick, polarized in the plane of incidence (p-polarized), a resonant absorption is observed just above 0. . For metals with loss loss at optical frequencies, particularly silver, the reflectance at the resonance angle may fall to practically zero, with a resonance width typically less than 0.5. Fig. 1 shows such a resonance in the reflectance curve for a film of silver. 

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. 

Spectral interferences in AAS arise mainly from overlap between the frequencies of a selected resonance line with lines emitted by some other element this arises because in practice a chosen line has in fact a finite bandwidth . Since in fact the line width of an absorption line is about 0.005 nm, only a few cases of spectral overlap between the emitted lines of a hollow cathode lamp and the absorption lines of metal atoms in flames have been reported. Table 21.3 includes some typical examples of spectral interferences which have been observed.47-50 However, most of these data relate to relatively minor resonance lines and the only interferences which occur with preferred resonance lines are with copper where europium at a concentration of about 150mgL 1 would interfere, and mercury where concentrations of cobalt higher than 200 mg L 1 would cause interference. 

In practice this condition may be fulfilled not only in excitation, e.g. by means of a pulsed laser or a continuous dye laser with insufficient frequency selectivity, but also by means of fines from a continuous gas laser working in simultaneous axial mode u>i (multimode) generation regime see Fig. 3.10(a). Let Au>i = u>i+1 — uii = itc/L denote the mode separation in a laser, L being the resonator length. Then, as pointed out in [110, 127, 231], broad line approximation works if Awj is smaller than the width of the Bennet holes r en [268, 320] in the absorption contour see Fig. 3.10(6). The positions of the Bennet holes are determined by the condition ujq — w/ + kv = 0, where luq is the central transition frequency, k is the wave vector and v is the velocity of the absorbing particle. The broad fine approximation is valid if the following conditions are fulfilled (see Fig. 3.10) ... 

As in the case of the artificial photo-absorption spectrum above, the spectrum cr E) features characteristic resonance profiles from which the positions and widths of all states, represented in the initial wave packet, can be extracted. If (0) overlaps with all eigenstates in a broad energy range, the entire spectrum can be recovered in a single calculation. In practical applications, the exponential operator (the propagator) in Eq. (14) is... 

The total number of unpaired electrons is proportional to the area under the spin-resonance line. The sensitivity of detection is increased if the absorption line is narrow and decreases to zero when it is so broad as to be indistinguishable against the background noise. For spin resonances whose width is of the order of 1 gauss at half-height, the practical limit of detection is about 10 mole of unpaired spins at 10,000 Me. The sensitivity increases with increase in frequency, being proportional to the square of the latter. On the other hand, dielectric losses which lower the sensitivity are smaller at the lower frequencies. Usually, the intensity of absorption increases with decrease in temperature, as would be expected from the Curie-Weiss law. 

Figure 1 is a sketch of the atomic absorption process. In lA, the emission spectrum of a hollow-cathode lamp is shown, with emission lines whose half-width is typically about 0.02 A. For most practical purposes, the desired element in the sample can be considered as being able to absorb only the "resonance lines, whose wavelengths correspond to transitions from the minimum energy state to some higher level. In IB, the sample is shown to absorb an amount "x which corresponds to the concentration of the element of interest. As seen in Figure 1C, after the flame, the resonance line is reduced while the others are unaflFected. In order to screen out the undesired emission, the radiation is now passed through a filter or monochromator (ID) which is tuned to pass the line... 

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