Absorption line width

Perhaps the first evidence for the breakdown of the Born-Oppenheimer approximation for adsorbates at metal surfaces arose from the study of infrared reflection-absorption line-widths of adsorbates on metals, a topic that has been reviewed by Hoffmann.17 In the simplest case, one considers the mechanism of vibrational relaxation operative for a diatomic molecule that has absorbed an infrared photon exciting it to its first vibrationally-excited state. Although the interpretation of spectral line-broadening experiments is always fraught with problems associated with distinguishing... 

The major requirement of the light source for atomic absorption is that it should emit the characteristic radiation (the spectrum) of the element to be determined at a half-width less than that of the absorption line. The natural absorption line width is about 10 4 (A), but due to broadening factors such as Doppler and collisional broadening, the real or total width for most elements at temperatures between 2000 ° and 3000 °K is typically 0.02 — 0.1 A. Hence, a high resolution monochromator is not required. 

Both the modes of operation described in Sect. 5.2 may be used for the detection of chemicals in liquid solution. Because the analyte s absorption line width is very broad, overlapping several (or many) WGMs, no tuning of the microresonator, or locking of a WGM to the scanning laser is necessary. In fact, a broadband source such as a light-emitting diode (LED) may be used. 

In order to determine the hydroxyl absolute concentrations by the linear absorption method, it is necessary to know the absorption line-width. This has become possible due to the work of Oldenberg and Itieke.4... 

Partial saturation of the HO absorption and use of excitation line widths wider than the HO absorption line width are in general undesirable, because they may produce spurious HO while exciting HO fluorescence with less than 100% efficiency (103). However, the issue is not as simple as matching the HO absorption profile exactly and avoiding all saturation. For instance, a matched laser excitation line width is more difficult to achieve and to keep tuned to the HO absorption, and the... 

Gaussian Laser Profile-Voigt Atom Profile. This case turns out to be a better approximation of our experimental situation, i.e., the laser FWHM is fairly broad compared to the absorption line width and the absorption profile of atoms in an atmospheric combustion flame is described by a Voigt profile. Here the laser is assumed to have a Gaussian spectral profile as well as a Gaussian atomic absorption profile. In this case, convolution of two Gaussian functions is still a Gaussian function. Evaluation of the ratio n2/nT, and the fluorescence radiance. Bp, allows determination of the half width of the fluorescence excitation profile, 6X... 

A major breakthrough came in Australia when Alan Walsh1,2 realized that light sources were available for many elements which emitted atomic spectral lines at the same wavelengths as those at which absorption occurred. By selecting appropriate sources, the emission line widths could be even narrower than the absorption line widths (Figure 2). Thus the sensitivity problem was solved more or less at a stroke, and the modern flame atomic absorption spectrometer was bom. 

Earlier an experiment was described in which atomic absorption lines were observed using a hydrogen lamp radiation source. Experimentally it can be shown that these absorption line widths are extremely narrow and can only be isolated under conditions of very high spectral resolution. 

The natural line width is the width of the absorption line not exposed to any broadening effects. It is a hypothetical case because the lines are essentially always broadened by experimental conditions. However the natural line width indicates the lower limit of the absorption lines width. It can be calculated from the uncertainty principle which states that... 

Atomic absorption offers a more practical opportunity for determining isotopic composition than atomic emission. Useful reviews of the possibilities of the technique have appeared in two books [233, 234]. Isotopic analysis is in theory possible provided that highly enriched isotope sources are available, the absorption line width available is less than the isotopic displacement and for a given isotope the nuclear spin hyperfine components must be partially resolved from the other isotopic components of the absorption line. In the simplest possible case, for an element with two isotopes, the lamp is prepared from the first isotope and only this isotope in the atom cell will absorb the radiation. The procedure can then be repeated with a lamp prepared with the second isotope. Effectively this is an extension of the impressive selectivity of atomic absorption, because of the classic lock and key effect, treating the different isotopes as different analytes. 

The pulsed NMR apparatus (12 MHz) and methods of procedure have been described previously (10, 13). The spin-spin relaxation time, T2, equivalent to the inverse absorption line width, is a time constant for the exponential decay toward internal equilibrium in the nuclear spin system. The spin-lattice relaxation time, Tu is the time constant for the exponential decay toward equilibrium between the nuclear spins and all other degrees of freedom of the system. The data are presented in Figure 1. Note that at higher temperatures T2 is much lower than Ti. 

The ability of atomic absorption to distinguish between elements and avoid spectral interferences does not depend on the monochromator. It depends instead on the emission line width of the hollow cathode lamp (typically 0.02A.), and the absorption line width of the element in the flame (typically 0.04A.). These values are far superior to the resolution capabilities of commonly available monochromators. Therefore, the monochromator does not enter directly into the ability of the atomic absorption instrument to give a specific result. See Figure 1.)... 

Dissociation rates can be determined by three methods which are based on (a) the measurement of relative rates, that is, the ratio of two rates one of whose rate constant is known (b) direct real-time rate measurements and (c) rate extraction from homogeneously broadened absorption line widths. The first two methods can be employed over very large time scales, whereas the last method is limited to rates in excess of about 10 sec E... 

It is important in AA measurements that the emission line width coming from the radiation source is narrower than the absorption line width of the atoms studied. In principle, a high resolution monochromator is not needed to separate the analyte line from the other lines of the spectrum, but in practice, the spectral bandpass of the source should be equal or less than the absorption line width. Otherwise, artificially low absorbance values are obtained leading to reductions in sensitivity. In the AA technique the use of continuum sources (quartz-halogen filament lamps and deuterium and xenon arc lamps) with reasonably priced monochromators is not satisfactory. This is demonstrated in Figure 17. In the case of (A) the emission of radiation is continuous for the whole spectral bandwidth. The energy absorbed by the atoms of the analyte is small in comparison to the whole... 

Figure 8.13 Mechanical and dielectric loss tangent tan 8 and NMR absorption line width (maximum slope, in gauss) of polytrifluorochloroethylene (Kel-F) (41).

Abstract. In this paper we find spatial and average dependences of the optical medium thickness, spectral profile and absorption line width on the initial thickness of the medium and the ratio between the hmiting velocity of self-similar expansion and the thermal velocity of atoms. 

In this paper we analyze the absorption spectrum characteristics (optical thickness, absorption line width and shape) in a self-similarly expanding gaseous sphere. 

Expressions (8) and (9) can provide spatial and mean estimates for the optical thickness of the medium and absorption line width and shape. 

The absorption line width is determined by the frequency range equal to double frequency difference between uj = 0 and wi corresponding to half maximum absorption. For the Doppler line shape... 

Fig. 6. Absorption line width for v = 0. "O — as obtained from (8), Curve 1 as formd...

Fig. 7. Absorption line width (top - = 0, bottom - averaged over tp). Curve 1 refers...

The absorption line width along the chord is determined by Auj (1 + 0 /3) for small alpha and by Au 2a for large a. Upon spatial averaging the coefficient in front of a decreases because of the changes in the velocity projection on the direction of radiation propagation. 

Under experimental conditions of temperature such that Zeeman energies are /cT, and where the Zeeman splitting is small compared with absorption line width, there can be three separate contributions to net ellipticity, imaginatively called A, B and C terms. The magnetically degenerate ground or excited states are split by the application of the external field, Hq. 

Substituting Equation [14] into Equation [13], assuming that Iq is invariant with wavelength over the absorption line width, and integrating over the... 

---