Linewidth, of spectral lines

An important consequence of the lineshape theory discussed above concerns the effect of the bath dynamics on the linewidths of spectral lines. We have already seen this in the discussion of Section 7.5.4, where a Gaussian power spectrum has evolved into a Lorentzian when the timescale associated with random frequency modulations became fast. Let us see how this effect appears in the context of our present discussion based on the Bloch-Redfield theory. 

All methods which allow the natural linewidth of spectral lines to be measured even in the presence of other broadening effects, may be used to obtain f values and Einstein coefficients. In this field, laser spectroscopy has brought a great variety of different Doppler-free techniques which will be discussed in Chap.10. A review of different methods of the prelaser era can be found in [2.18a,b]. 

The most ftmdamental limitation on sharpness of spectral lines is the so-called natural linewidth. Because an... 

The spectral linewidths of fluorescence lines are determined in most spectral lamps by Doppler effect and pressure broadening and are therefore normally much broader than the natural linewidth, which is approached only by low-pressure hollow cathode lamps 23) operated at liquid helium temperatures. 

Inspection of the spectral shapes in Fig. 4 indicates that the linewidth of the six-line component due to the inner radical becomes sharpened with t2. This spectral sharpening is interpreted as being due to the dependence of the relaxation rate on the resonance frequency the relaxation is slower for the radicals at or near the peak of spectral lines than that for the radicals at the spectral tail because of the angular dependence of the hyperfine coupling. 

Direct spectral line interference occurs when the spectral line energy of two or more elements reaches the detector circuit. One type of spectral line interference involves spectral line overlap. This occurs because spectral lines have a finite linewidth. If the spectral energies of two lines overlap, the result is spectral interference regardless of the resolving power of the spectral isolation system of the spectrometer. At high flame temperatures, when... 

The instrumental resolution of the spectrometers is limited by the combined frequency fluctuation from each CO2 laser (about 15 kilohertz). This, of course, is less than any Doppler limited linewidth and, therefore, does not limit our resolution except for possible sub-Doppler work. This high resolution provides an excellent way of studying pressure shifts and line shape studies of spectral lines. The measurement of OH concentrations in our atmosphere as a function of altitude using absorption and emission measurements requires an accurate knowledge of its linewidth in the atmosphere. 

There is a second effect that causes a collisional narrowing of spectral lines. In the case of very long lifetimes of levels connected by an EM transition, the linewidth is determined by the diffusion time of the atoms out of the laser beam (Sect. 3.4). Inserting a noble gas into the sample cell decreases the diffusion rate and therefore increases the interaction time of the sample atoms with the laser field, which results in a decrease of the linewidth with pressure [3.36] until the pressure broadening overcompensates the narrowing effect. 

It is important to realize that the relaxation times might depend on some factors that are properties of the atom or molecule itself and on others that are related to its environment. Thus rotational spectra of gases have linewidths (related to the rotational relaxation times) that depend on the mean times between coUisions for the molecules, which in turn depend on the gas pressure. In liquids, the collision lifetimes are much shorter, and so rotational energy is effectively non-quantized. On the other hand, if the probability of collisions is reduced, as in a molecular beam, we can increase the relaxation time, reduce linewidths, and so improve resolution. Of course, the relaxation time only defines a minimum width of spectral lines, which may be broadened by other experimental factors. 

In many cases, the spectral width of the gain profile is comparable with that of spectral lines from incoherent spectral lamps, as, for example, is the case for gas lasers with gain profiles determined by the Doppler width of the amplifying transition between two discrete states of excited atoms or molecules in the active medium. Also, in many solid-state lasers, where the active medium is composed of excited impurity atoms or ions, diluted at low concentrations in a host crystal lattice, the linewidth of the amplifying transition is often small compared with the commonly found broad absorption bands of solids. In such cases the laser wavelength is restricted... 

The adiabatic theory enables quite accurate theoretical estimates of the broadening and shift of spectral lines to be made in simple cases. For interaction potentials of the form it predicts a unique ratio of linewidth to line... 

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. 

The sinc fiinction describes the best possible case, with often a much stronger frequency dependence of power output delivered at the probe-head. (It should be noted here that other excitation schemes are possible such as adiabatic passage [9] and stochastic excitation [fO] but these are only infrequently applied.) The excitation/recording of the NMR signal is further complicated as the pulse is then fed into the probe circuit which itself has a frequency response. As a result, a broad line will not only experience non-unifonn irradiation but also the intensity detected per spin at different frequency offsets will depend on this probe response, which depends on the quality factor (0. The quality factor is a measure of the sharpness of the resonance of the probe circuit and one definition is the resonance frequency/haltwidth of the resonance response of the circuit (also = a L/R where L is the inductance and R is the probe resistance). Flence, the width of the frequency response decreases as Q increases so that, typically, for a 2 of 100, the haltwidth of the frequency response at 100 MFIz is about 1 MFIz. Flence, direct FT-piilse observation of broad spectral lines becomes impractical with pulse teclmiques for linewidths greater than 200 kFIz. For a great majority of... 

Its temporal coherence, causing spectral linewidths of the induced emission to be smaller by several orders of magnitude than those of fluorescence lines emitted by spectral lamps. 

The width of the spectral line equals the sum of the widths of initial and final levels. Due to the short lifetime of highly excited states with an inner vacancy, their widths, conditioned by spontaneous transitions, are very broad. The other reasons for broadening of X-ray and electronic lines (apparatus distortions, Doppler and collisional broadenings) usually lead to small corrections to natural linewidth. 

In general, it may be expected that the sites for Fe2+ and Fe3+ in these noncrystalline ion exchange resins will have a large distribution of chemical environments. This expectation should be reflected as a significant broadening of the Mbssbauer resonance, as experimentally observed by Johansson 188). In addition, this broadening should result in a non-Lorenzian spectral line shape. Indeed, a computer analysis of the spectra showed that Gaussian peaks provided a better fit of the data than did Lorenzian peaks. In this case then, the linewidth and peak shape provide information about the distribution of support interactions for the various resonant atoms in the sample. 

Recently, Cottam and Ward (182) found that with the titration of apo-alkaline phosphatase with Zn(II) up to a mole ratio of four Zn(II/ dimer results in no increase in the S5C1 NMR linewidth, .. . while in previous studies of zinc activated biological reactions, a large increase in the chloride linewidth was observed with zinc bound to macromolecules. However, an increase in the chloride linewidth is observed when the pH is decreased below 5.0. This was interpreted as showing that Zn(II) in alkaline phosphatase is not exposed to solvent at pH > 5.0. In an ESR study of Cu(II) binding to alkaline phosphatase, Csopak and Falk (133) reported that two Cu(II) binds to the same specific sites as the two Zn(II), that the ESR spectrum for the one copper enzyme is different from the two copper enzymes, and that phosphate binding causes a shift of the spectral lines. 

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