Line width transition

Figure 1. Relation of line width, transition energy, and recoil energy, (a) Overlap (schematic) of emission and absorption lines in optical transitions, (b) Absence of overlap (schematic) of emission and absorption lines in nuclear transitions involving atoms free to recoil. Drawn to scale, separation between two lines would be about 4 X 10 the width of each line at half rriaximum...

Figure 15.4—Line width. Transition between a stable ground state having an infinite lifetime and an excited state, which is short-lived. The uncertainty in AE2 induces an imprecision on the corresponding wavelength.

In practice the laser can operate only when n, in Equation (9.2), takes values such that the corresponding resonant frequency v lies within the line width of the transition between the two energy levels involved. If the active medium is a gas this line width may be the Doppler line width (see Section 2.3.2). Figure 9.3 shows a case where there are twelve axial modes within the Doppler profile. The number of modes in the actual laser beam depends on how much radiation is allowed to leak out of the cavity. In the example in Figure 9.3 the output level has been adjusted so that the so-called threshold condition allows six axial modes in the beam. The gain, or the degree of amplification, achieved in the laser is a measure of the intensity. 

The ability to measure the energy of electronic transitions and their line widths accurately, in a convenient manner, is one of the most important aspects of semiconductor characterization. The former can be used to evaluate alloy compositions... 

The formation of monomer and dimer of (salen)Co AIX3 complex can be confirmed by Al NMR. Monomer complex la show Al NMR chemical shift on 5=43.1 ppm line width =30.2 Hz and dimer complex lb 5=37.7 ppm line width =12.7 Hz. Further instrumental evidence may be viewed by UV-Vis spectrophotometer. The new synthesized complex showed absorption band at 370 nm. The characteristic absorption band of the precatalyst Co(salen) at 420 nm disappeared (Figure 1). It has long been known that oxygen atoms of the metal complexes of the SchifT bases are able to coordinate to the transition and group 13 metals to form bi- and trinuclear complex [9]. On these proofs the possible structure is shown in Scheme 1. 

Fig. 2.2 Intensity distribution /( ) for the emission of y-rays with mean transition energy Eq. The Heisenberg natural line width of the distribution, F = S/t, is determined by the mean lifetime T of the excited state (e)...

The emission spectmm of Co, as recorded with an ideal detector with energy-independent efficiency and constant resolution (line width), is shown in Fig. 3.6b. In addition to the expected three y-lines of Fe at 14.4, 122, and 136 keV, there is also a strong X-ray line at 6.4 keV. This is due to an after-effect of K-capture, arising from electron-hole recombination in the K-shell of the atom. The spontaneous transition of an L-electron filling up the hole in the K-shell yields Fe-X X-radiation. However, in a practical Mossbauer experiment, this and other soft X-rays rarely reach the y-detector because of the strong mass absorption in the Mossbauer sample. On the other hand, the sample itself may also emit substantial X-ray fluorescence (XRF) radiation, resulting from photo absorption of y-rays (not shown here). Another X-ray line is expected to appear in the y-spectrum due to XRF of the carrier material of the source. For rhodium metal, which is commonly used as the source matrix for Co, the corresponding line is found at 22 keV. 

Potzel et al. [60] used a Ga/ZnO single crystal source in combination with a single crystal absorber of natural ZnO and observed a resonance line width of 0.36 0.04 pm s for the 93.3 keV transition in Zn (at 4.2 K). This, after correction for finite absorber thickness, equals, within the limit of error, the minimum observable line width as deduced from the lifetime of 13.4 ps for the 93.3 keV state. The spectra observed by these authors are shown in Fig. 7.23. 

Potzel et al. [Ill] have established recoil-free nuclear resonance in another ruthenium nuclide, ° Ru. This isotope, however, is much less profitable than Ru for ruthenium chemistry because of the very small resonance effect as a consequence of the high transition energy (127.2 keV) and the much broader line width (about 30 times broader than the Ru line). The relevant nuclear properties of both ruthenium isotopes are listed in Table 7.1 (end of the book). The decay... 

Nuclear resonance absorption for the 136 keV transition has been established by Steiner et al. [174]. The authors used a metal source and an absorber of metallic tantalum to determine the mean lifetime of the 136 keV level from the experimental line width ( 52.5 mm s for zero effective absorber thickness) and found a value of 55 ps. This has been the only report so far on the use of the 136 keV excited state of Ta for Mossbauer experiments. 

Table 7.5 ° Ta isomer shift, experimental line width and resonance effect, observed for sources of diffused into various transition metal hosts against tantalrun metal as absorber, and for...

Table 7.8 Summary of results obtained for the four Os Mossbauer transitions studied. The absorber thickness d refers to the amount of the resonant isotope per unit area. The estimates of the effective absorber thickness t are based on Debye-Waller factors / for an assumed Debye temperature of 0 = 400 K. For comparison with the full experimental line widths at half maximum, Texp, we give the minimum observable width = 2 S/t as calculated from lifetime data.

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. 

It is much more difficult to observe the Mossbauer effect with the 130 keV transition than with the 99 keV transition because of the relatively high transition energy and the low transition probability of 130 keV transition, and thus the small cross section for resonance absorption. Therefore, most of the Mossbauer work with Pt, published so far, has been performed using the 99 keV transition. Unfortunately, its line width is about five times larger than that of the 130 keV transition, and hyperfine interactions in most cases are poorly resolved. However, isomer shifts in the order of one-tenth of the line width and magnetic dipole interaction, which manifests itself only in line broadening, may be extracted reliably from Pt (99 keV) spectra. 

Typical absorbers contain 50-700 mg cm of natural platinum. The observed experimental line widths in Pt (99 keV) spectra range from values close to the natural width (2F at (99 keV) = 16.28 mm s ) to 25 mm s. With respect to the line width, the 130 keV transition with a natural width of (130 keV) = 3.40 mm s seems to be more favorable for the study of hyperfine interaction in platinum compounds in practice, experimental line widths of 3.4 0.4 [328] and 3.5 0.7 mm s [329] have been measured. The considerably higher energy resulting in a much smaller recoiUess fraction and the lower probability for the population... 

The first clear resonance effect using the 130 keV transition in Pt was observed on a platinum metal absorber by Wilenzick et al. [328] (resonance effect 0.16%, line width 4.4 0.4 mm s ) and by Wolbeck and Zioutas [324] (resonance effect 0.044%, line width 2.6 1.5 mm s ). Considerably improved... 

The first Mossbauer measurements involving mercury isotopes were reported by Carlson and Temperley [481], in 1969. They observed the resonance absorption of the 32.2 keV y-transition in (Fig. 7.87). The experiment was performed with zero velocity by comparing the detector counts at 70 K with those registered at 300 K. The short half-life of the excited state (0.2 ns) leads to a natural line width of 43 mm s Furthermore, the internal conversion coefficient is very large (cc = 39) and the oi pj precursor populates the 32 keV Mossbauer level very inefficiently ( 10%). 

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