Line-width

The ubiquitous use of the word Tine to describe an experimentally observed transition goes back to the early days of observations of visible spectra with spectroscopes in which the lines observed in, say, the spectmm of a sodium flame are images, formed at various wavelengths, of the entrance slit. Although, nowadays, observations tend to be in the form of a plot of some measure of the intensity of the transition against wavelength, frequency or wavenumber, we still refer to peaks in such a spectmm as lines. 

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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. 

Avdievich N I and Forbes M D E 1995 Dynamic effects in spin-correlated radical pair theory J modulation and a new look at the phenomenon of alternating line widths in the EPR spectra of flexible biradicals J. Phys. Chem. 99 9660-7... 

Figure C 1.3.5. Spectra of two different infrared bands of HF dimer, corresponding to excitation of the bound (lower panel) and free (upper panel) HF monomers in the complex. Note the additional line width for the bound HF, caused by vibrational predissociation with a lifetime of about 0.8 ns. (Taken from 1211.)...

Another feature of the spectrum shown in Figure 10.19 is the narrow width of the absorption lines, which is a consequence of the fixed difference in energy between the ground and excited states. Natural line widths for atomic absorption, which are governed by the uncertainty principle, are approximately 10 nm. Other contributions to broadening increase this line width to approximately 10 nm. 

Equation 10.1 has an important consequence for atomic absorption. Because of the narrow line width for atomic absorption, a continuum source of radiation cannot be used. Even with a high-quality monochromator, the effective bandwidth for a continuum source is 100-1000 times greater than that for an atomic absorption line. As a result, little of the radiation from a continuum source is absorbed (Pq Pr), and the measured absorbance is effectively zero. Eor this reason, atomic absorption requires a line source. 

Figure 2.5 shows, for a sample in the gas phase, a typical absorption line with a HWHM (half-width at half-maximum) of Av and a characteristic line shape. The line is not infinitely narrow even if we assume that the instmment used for observation has not imposed any broadening of its own. We shall consider three important factors that may contribute to the line width and shape. 

Of the four types of broadening that have been discussed, that due to the natural line width is, under normal conditions, much the smallest and it is the removal, or the decrease, of the effects of only Doppler, pressure and power broadening that can be achieved. 

Molecules such as 3,4 and 5 in Figure 2.6, which have a zero velocity component away from the source, behave uniquely in that they absorb radiation of the same frequency Vj-es whether the radiation is travelling towards or away from R, and this may result in saturation (see Section 2.3.4). If saturation occurs for the set of molecules 3, 4 and 5 while the radiation is travelling towards R, no further absorption takes place as it travels back from R. The result is that a dip in the absorbance curve is observed at Vj-es, as indicated in Figure 2.5. This is known as a Lamb dip, an effect which was predicted by Lamb in 1964. The width of the dip is the natural line width, and observation of the dip results in much greater accuracy of measurement of v es. 

Until the advent of lasers the most intense monochromatic sources available were atomic emission sources from which an intense, discrete line in the visible or near-ultraviolet region was isolated by optical filtering if necessary. The most often used source of this kind was the mercury discharge lamp operating at the vapour pressure of mercury. Three of the most intense lines are at 253.7 nm (near-ultraviolet), 404.7 nm and 435.7 nm (both in the visible region). Although the line width is typically small the narrowest has a width of about 0.2 cm, which places a limit on the resolution which can be achieved. 

Lasers (see Chapter 9) are sources of intense, monochromatic radiation which are ideal for Raman spectroscopy and have entirely replaced atomic emission sources. They are more convenient to use, have higher intensity and are more highly monochromatic for example, the line width at half-intensity of 632.8 nm (red) radiation from a helium-neon laser can be less than 0.05 cm. ... 

Because the line width is much less than the resolution this ratio is not reflected in the peak heights in Figure 6.8. 

A monochromator is useful not only for removing unwanted lines from the X-ray source but also for narrowing the otherwise broad lines. For example, each of the MgXa and AlXa doublets is unresolved and about 1 cY wide at half-intensity. A monochromator can reduce this to about 0.2 cY This reduction of the line width is very important because in an XPS specttum, unlike an ultraviolet photoelectron specttum, the resolution is limited by the line width of the ionizing radiation. Unfortunately, even after line narrowing to 0.2 cY... 

Figure 9.3 Doppler limited laser line with twelve axial modes within the line width...

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. 

An important consequence of shortening a laser pulse is that the line width is increased as a result of the uncertainty principle as stated in Equation (1.16). When the width of the pulse is very small there is difficulty in measuring the energy precisely because of the rather small number of wavelengths in the pulse. For example, for a pulse width of 40 ps there is a frequency spread of the laser, given approximately by (2 iAt), of about 4.0 GFIz (0.13 cm ). 

Laser radiation is very much more intense, and the line width much smaller, than that from, for example, a mercury arc, which was commonly used as a Raman source before 1960. As a result, weaker Raman scattering can now be observed and higher resolution is obtainable. 

Dye lasers, frequency doubled if necessary, provide ideal sources for such experiments. The radiation is very intense, the line width is small ( 1 cm ) and the wavenumber may be tuned to match any absorption band in the visible or near-ultraviolet region. 

In a skimmed supersonic jet, the parallel nature of the resulting beam opens up the possibility of observing spectra with sub-Doppler resolution in which the line width due to Doppler broadening (see Section 2.3.4) is reduced. This is achieved by observing the specttum in a direction perpendicular to that of the beam. The molecules in the beam have zero velocity in the direction of observation and the Doppler broadening is reduced substantially. Fluorescence excitation spectra can be obtained with sub-Doppler rotational line widths by directing the laser perpendicular to the beam. The Doppler broadening is not removed completely because both the laser beam and the supersonic beam are not quite parallel. 

In order to observe such high-resolution fluorescence excifafion spectra, the laser must have a very small line width. To achieve this a ring dye laser, a modification of the dye laser described in Section 9.2.10, is used a line width as small as 0.5 MFIz (1.5 x 10 cm ) can be obtained. 

If dye molecules are embedded into an amorphous matrix, preferably transparent polymers, greatly and inbornogenously broadened spectral lines are observed. This broadening is caused by the energetic interaction of the dye molecules with the locally different environment in the polymer matrix. The ratio of the homogenous initial line width of the dye molecule T to the inhomogenous line width of the dye in the polymer T ranges from 1 10 to 1 10 . ... 

Because of the narrow line width, absorption of laser energy can excite one specific state in an atom or molecule. The laser is tuned so that its wavelength matches an absorption corresponding to the desired state, which may be an electronic state or vibrational state. Absorption of laser energy can lead to excitation of specified states much more effectively than absorption of light from conventional light sources. 

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