Resonant absorption coefficient

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. 

We have limited our investigations to the action of gamma-rays and fast neutrons on aromatic, alicyclic, aliphatic, and ionic compounds. The absorption coefficients for these types of radiation have an order of magnitude of lO /cm which is particularly adequate. Shallow penetrating radiations would only alter the superficial layers and would obviously not be able to affect the intensity of the quadrupole line substantially. This is for instance the case for ultraviolet light which has been shown to be unable to produce any effect on the resonance line of iodoform (CHI3 3Sg)... 

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%). 

If we express the effective thickness t for the resonant absorption in terms of the total absorber thickness t in g cm, a nuclear absorption coefficient can be defined in cm g such that = t. The signal amplitude is then given by ... 

To avoid this handicap, Boersch and coworkers 2) used coupled resonators. The first active laser cavitiy generates the radiation whose absorption is to be measured. The probe is placed in a second cavity, which is coupled to the first one and which is undamped by an active medium just below the threshold for self-oscillation. This arrangement enables changes in the refractive index as small as An 10 ° or absorption coefficients down to a 10 to be detected. 

Measurement of non-linear optical properties [580] also provides a means for characterizing size-quantized semiconductor particles. Third-order optical non-linearity of size-quantized semiconductor particles has been discussed in terms of resonant and non-resonant contributions [11]. Resonant non-linearity is expected to increase with decreasing particle size and increasing absorption coefficients. 

Microwaves. Among the lowest frequencies of interest in collisional absorption are radio- and microwaves. As will be seen below, the absorption coefficient a is extremely small at low frequencies because absorption falls off to zero frequency as of2 see Chapter 5 for details. As a consequence, it has generally been necessary to use sensitive resonator techniques for the measurement of the loss tangent, tan <5 = s"/s, where s and s" are the real and imaginary part of the dielectric constant. The loss tangent is obtained by determination of the quality factors Qa, Qo, of the cavity with and without the gas filling, as (Dagg 1985)... 

Intercollisional interference. We note that at the lowest frequencies the simple proportionality between absorption coefficient and product of gas densities breaks down. Under such conditions, certain many-body interactions affect the observations and modify the shape or intensities of the binary spectra, often quite strikingly. An example is shown in Fig. 3.3, a measurement of the absorption in a neon-xenon mixture in the microwave region, at the fixed frequency of 4.4 cm-1. Because of the frequency-dependent factor of g(v) that falls off to zero frequency as v2, absorption is extremely small at such frequencies, Eq. 3.2. As a consequence, it has generally been necessary to use sensitive resonator techniques for a measurement of the absorption at microwave frequencies... 

The paper of 1939 [1 ], On the Chain Decay of the Main Uranium Isotope, studies the effects of elastic and non-elastic neutron moderation and concludes that chain fission reactions by fast neutrons in pure metallic natural uranium are impossible. The 1940 paper, On the Chain Decay of Uranium under the Influence of Slow Neutrons [2 ], is classic in the best sense of this word its value is difficult to overestimate. The theoretical study performed showed clearly that the effect of resonance absorption of neutrons by nuclei of 238U is a governing factor in the calculation of the coefficient of neutron breeding in an unbounded medium it was concluded that a self-sustained chain reaction in a homogeneous natural uranium-light water system is impossible. 

The absorption coefficient, of mercury vapor for a Doppler-broadened resonance line is given by the expression ... 

The nonlinear refractive index, r, linear absorption, a, and two photon absorption coefficient, jS, of metal dithiolenes and rare earth metallocenes have been measured at 1064 nm using 100 ps and 10 ns pulses. These measurements have shown resonance enhanced molecular nonlinearities of 10M05 times those of carbon disulphide can be obtained. Figures of merit based on the nonlinear refractive index and the linear and two photon absorption coefficients are within the limits required for devices. 

Apparently monochromatic resonance radiation of mercury which passes through mercury vapor at the saturated pressure at 25 °C is about half absorbed in four millimeters distance. Beer s law is not obeyed at all because the incident radiation cannot be considered to be actually monochromatic, and absorption coefficients of mercury vapor vary many times between zero and very high values in the very short space of one or two hundredths of an Angstrom unit. Moreover, absorption of mercury resonance radiation by mercury vapor is sufficiently great even at room temperature to make radiation imprisonment a very important phenomenon. If the reaction vessel has any dimension greater than a few millimeters the apparent mean life of Hg(63P ) may be several fold the true radiative life of 1.1 x 10"7 sec, reaction (27), because of multiple absorption and re-emission. 

In Fig. 34c (for H20) and Fig. 34d (for D20), solid lines show the absorption coefficients a calculated in the R-band the estimated contributions to this a(v) due to reorientations and vibrations are shown by dashed and dashed-and-dotted curves, respectively. The resonance peak at vR 200 cm-1 found for both water isotopes is actually determined by a vibrating nonrigid dipole. The distinction between the curves calculated for ordinary and heavy water is substantial. In the case of H20, Fig. 34c, the contributions of reorientations and vibrations to the resulting a(v) curve are commensurable near the center of the R-absorption peak, while in the case of D20 (Fig. 34d) the main contribution to ot(v) near the R-band peak comes from vibration of the H-bonded molecules. 

Several reductive assays have been proposed (Table 3). A test using reduction of l,l-diphenyl-2-picrazyl (DPPH) radical was introduced in the 1950s (B15) and has been used by various authors. DPPH is a stable free radical, which can be bought in substantia. It has an absorbance maximum at 515 nm (millimolar absorption coefficient e = 12.5 mM-1 cur1) (A15). A disadvantage of this chromogen lies in the fact that it can be dissolved only in organic (especially alcoholic) but not in aqueous media, which limits its use for studies of hydrophilic antioxidants. Reduction of ABTS also can be followed by electron spin resonance (ESR) (Yl). 

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