Width atomic linewidth

High-resolution spectroscopy used to observe hyperfme structure in the spectra of atoms or rotational stnicture in electronic spectra of gaseous molecules connnonly must contend with the widths of the spectral lines and how that compares with the separations between lines. Tln-ee contributions to the linewidth will be mentioned here tlie natural line width due to tlie finite lifetime of the excited state, collisional broadening of lines, and the Doppler effect. 

Fig. 6 mCd NMR chemical shifts (diamonds) and linewidths (triangles) of Cd, YZ.nYTc as a function of x. The dashed-dotted line is the most probable number of NNN Zn atoms, and the solid line is the width calculated from probability distributions. Reprinted with permission from [157]. Copyright 1987 by the American Physical Society... 

The reason why one chose to follow the main liquid-crystalline to gel phase transition in DPPC by monitoring the linewidth of the various or natural abundance resonance is evident when we consider the expressions for the spin-lattice relaxation time (Ti) and the spin-spin relaxation time T2). The first one is given by 1/Ti oc [/i(ft>o) + 72(2ft>o)] where Ji coq) is the Fourier transform of the correlation function at the resonance frequency o>o and is a constant related to internuclear separation. The relaxation rate l/Ti thus reflects motions at coq and 2coq. In contrast, the expression for T2 shows that 1/T2 monitors slow motions IjTi oc. B[/o(0) -I- /i(ft>o) + /2(2u>o)], where /o(0) is the Fourier component of the correlation function at zero frequency. Since the linewidth vi/2 (full-width at half-maximum intensity) is proportional to 1 / T2, the changes of linewidth will reflect changes in the mobility of various carbon atoms in the DPPC bilayer. 

With this technique the Doppler width could be reduced by two orders of magnitude below the natural linewidth, and spectral structures within the Doppler width could be resolved. Examples are the resolution of hyperfine structure components in an 12-beam using a single-mode argon laser (tunable within a few gigahertz) or the investigation of the upper state hfs-splitting in the atomic... 

Beer s law requires that the linewidth of the radiation source should be substantially narrower than the linewidth of the absorbing sample. Otherwise, the measured absorbance will not be proportional to the sample concentration. Atomic absorption lines are very sharp, with an intrinsic width of only 10 4 nm. 

In most optical excitations the resolution is determined by the Doppler effect or the finite linewidth of the light source. The Doppler effect gives a typical frequency width of 1 GHz, and the width of the light source can be anywhere from 1 kHz to 30 GHz. We assume that these widths are larger than the radiative width. The photoionization cross sections from the ground states of H, alkali, and the alkaline earth atoms are given in Table 3.3. 20... 

The first and most obvious question is whether or not a narrower velocity distribution leads to narrower collisional resonances. In Fig. 14.14 we show the Na 26s + Na 26s — Na 26p + Na 25p resonances obtained under three different experimental conditions.20 In Fig. 14.14(a) the atoms are in a thermal 670 K beam. In Figs. 14.14(b) and (c) the beam is velocity selected using the approach shown in Fig. 14.13 to collision velocities of 7.5 X 103 and 3.8 X 103 cm/s, respectively. The dramatic reduction in the linewidths of the collisional resonances is evident. The calculated linewidths are 400, 28, and 10 MHz, and the widths of the collisional resonances shown in Figs. 14.14(a)-(c) are 350,40, and 23 MHz respectively. The widths decrease approximately as l/v3/2 until Fig. 14.14(c), at which point the inhomogeneities of the electric field mask the intrinsic linewidth of the collisional resonance. 

The lifetime of a separate atom in its ground state is infinite, therefore the natural width of the ground level equals zero. Typical lifetimes of excited states with an inner vacancy are of the order 10-14 — 10 16 s, giving a natural width 0.1 — 10 eV. The closer the vacancy is to the nucleus, the more possibilities there are to occupy this vacancy and then the broader the level becomes. That is why T > Tl > Tm- Generally, the total linewidth T is the sum of radiative (Tr) and Auger (T ) widths, i.e. 

Effective nuclear charge grows with increase of ionization and excitation of an atom, therefore, the fluorescence yield in ions and, to a less extent, in excited atoms, tends to increase. Radiative and Auger linewidths, as well as fluorescence yields, depend on relativistic and correlation effects to less extent in comparison with the probabilities of separate transitions, because in sums the individual corrections partly compensate each other. Therefore, calculations of radiative widths in the Hartree-Fock-Pauli approach lead to reasonably accurate results. 

Inertinite radicals have very uniform g values, the magnitude of which suggests association with aromatic molecules. Radical densities can be extremely high (up to 25 x the levels seen in exinites). The linewidths are much narrower than in other maceral types ( l-2 Gauss vs 7 G for exinites and vitrinites), and both widths and shapes depend sensitively on the maceral "history", as reflected in atomic H/C ratios and the density. 

The cavity is tuned by maximizing the atomic transfer rate. By this way, the cavity center frequency equals Fc within about 25% of the cavity resonance half-width. The slow variation of the MW power through the linewidth shifts the line in direction of the cavity center frequency. Since the cavity has a rather low quality factor, this shift is at the worst 500 Hz. Due to thermal drift, the cavity tuning may vary at the time scale of an hour, and yield a time-dependent 500 Hz systematic. 

Atomic absorption spectroscopy (AAS) was practiced in the mid-nineteenth century by passing a small sample into a flame and noting the color of the flame. Compared to molecular absorption, atomic absorption lines are very narrow. The linewidth is defined as the width of the signal at halfheight Ali/i, which for atoms is of the order of 0.002-0.005 nm. Al /2 consists of the natural linewidth plus the Doppler37 linewidth. 

Doppler linewidth, AX (equation (8.4)), hence the most sensitive lines are those which combine a narrow linewidth with a large oscillator strength. A wide range of linear response is attained if the width of the emission line is less. than one-fifth that of the absorption line. Guides to the appropriate choice of emission line are given in most standard texts on atomic absorption spectrometry. 

A low-pressure atomic emission lamp such as neon or argon emits atomic lines of sufficiently narrow linewidth to be considered infinitely narrow for most Raman spectrometers (an example is shown in Fig. 10.1). The width of atomic emission lines depends on temperature and pressure, but is generally... 

Figure 11.8. A. Width of the NMR resonance of various cubic Nii Alx alloys as a function of temperature. Note that only the highest-Ni alloy Nio.46 AI0.54 shows a significant change in linewidth with temperature. B. Temperature dependence of the Al powder lineshape of Ni2Ala. Note the evolution of the 2 room-temperature overlapping quadmpole lineshapes into a single line as the aluminium atoms jump between the 2 sites with increasing temperature.

Eq. (8) is given in atomic units, and if we re-express it in laboratory units, for n = 20, we find a = 3.10-8 cm2 and r = 10-9 s. This value of the cross section is in accord with our earlier rough estimate, and the inverse of the collision time is consistent with the linewidths of the collisional resonances shown in Fig. 2. The n scaling of both the cross section and the resonance width has been verified, and in Fig. 3 we show the observed dependence of the width A of the (0, 0) resonance on n [Gallagher 1982],... 

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