Spectral linewidth

According to the Bohr model of the atom, atomic absorption and emission linewidths should be infinitely narrow, because there is only one discrete value for the energy of a given transition. However, there are several factors that contribute to line broadening. The natural width of a spectral line is determined by the Heisenberg uncertainty principle and the lifetime of the excited state. Most excited states have lifetimes of s, 

As discussed in Chapter 2, the fraction of incident light absorbed by a species can be expressed as the absorbance, A. The relationship between absorbance and the amount of analyte, in this case, atoms, in the light path is given by Beer s law  

The proportionality constant a is called the absorptivity and includes the oscillator strength / The term b is the length of the light path and c is the concentration of ground-state atoms in the light path (i.e., atoms/cm ). 

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Siagle-mode operation is usually achieved at the expense of output power. Very-high-power lasers are usually not available as siagle-mode lasers, and an iacrease of power is usually accompanied by an iacrease ia the spectral linewidth. 

Fe Q-band ENDOR study of the isotopically enriched Ni-C state of D. gigas and D. desulfuricans hydrogenases and Ni-B state of D. desulfuricans revealed a weak coupling between the Fe and the nickel atoms when the enzyme was in the Ni-A forms while no coupling was observed for the Ni-B form (186). A careful analysis of linewidth of Ni-A and Ni-B EPR signals detected in Fe enriched and nonenriched hydrogenase samples indicated that hyperfine interactions are lost in the spectral linewidth and, hence, nonde-tectable. 

Up to now, we have dealt only with the static effects of the spin-spin interactions. These effects are no longer observed when the splitting SB of the resonance lines due to these interactions is much smaller than the spectral linewidth or when the spin-lattice relax-... 

Table 4.2. The basic parameters of the models under discussion for some adsorption systems. The dephasing (2f 4)) and the relaxation (2T 3)) contributions to the full spectral linewidth for local vibrations as well as the...

Several general observations can be made from the spectra and the calculated ESR parameters. First, the Na+- smectites possess narrower resonance line widths than the Ca +-smectites, with the exception of the saponite. Since Ca +-smectites, unlike Na+ -smectites, do not disperse into individual platelets in aqueous suspension, the Na+-smectite films formed by drying suspensions onto a smooth flat surface have the silicate surfaces more perfectly oriented in the plane of the film. As a result, less angular variation of the z-axis of Cu + relative to the plane of the film would narrow the spectra. One can see evidence of hyperfine splitting in the gj component of the Na+-smectite spectra, but not in the Ca +-smectite spectra. Saponite, unlike the other smectites, has very similar spectral linewidths for the Na+ and Ca + form (Figure 16). Since this Na+-saponite sample does not disperse completely in water (Table II), the alignment of Na+-saponite platelets in the clay film may be no better than that of the Ca +-saponite. 

Another major application for microresonators is in development and fabrication of novel light sources such as resonant-cavity-enhanced light-emitting diodes (LEDs), low-threshold microlasers, and colour flat-panel displays. In wavelength-sized microresonator stmctures, semiconductor material luminescence can be either suppressed or enhanced, and they also enable narrowing of the spectral linewidth of the emitted light (Haroche, 1989 Yokoyama, 1992 Yamamoto, 1993 Krauss, 1999 Vahala, 2003). 

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 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. 

For a 1 the scattered light spectrum is gaussian with a width determined by the electron temperature, because it is due to the incoherent sum of Thomson scattering from individual, thermally moving electrons. The intensity and spectral linewidth of scattered light therefore yield electron density and temperature. 

The temperature dependencies of the soft mode frequency (closed symbols) and spectral linewidths (open symbols) in ST016, ST018-23, and ST018-32 are presented in Fig. 17a-c [27]. The crosses in Fig. 17a denote the temperature dependence of the soft mode frequency observed by hyper-Raman scattering. The results shown in Fig. 17 clearly indicate a decrease in... 

When Ad is observable, but much less than the difference between Si(nAl) and [Si(n 1)A1] chemical shifts, a broadening of the spectral linewidths is observed. For example, the 29Si spectrum of chemically untreated mordenite is broad because it is a superimposition of four sets of signals. 

The lifetime of the simplest quasiparticle, i.e. a hole in a surface band, can be obtained experimentally from the width of the corresponding peak in ARPES, since the spectral linewidth of a quasiparticle excitation in the energy space is inversely related to its lifetime. The lower panel of Fig. 4 shows the widths of the photoemission peaks at normal emission corresponding to the L-gap surface states. It can be shown [45] that for a 2D band such as these, the widths reflect the initial state (hole) lifetime. For these surface states the lifetime ranges from 30 to 110 femtoseconds (ImeV corresponds to a lifetime of 0.67 x 10 12s). 

In the definition of line broadening it is necessary to exercise some discrimination. On the one hand spectral linewidths of less them 0.17 cm-1 are observed for some of the vibronic bands of the lowest singlet system of benzene 1f 2 - -1diff in the vapor phase W, while on the other hand many electronic spectra have been encountered, in particular in higher excited singlet and triplet systems, for which few or no vibrational features are apparent. In crystal spectra at 4 K, linewidths as sharp as 0.5 cm-1 are often obtained for the lowest excited state of any multiplicity, despite coupling with the lattice modes, which may be expected to lead to considerable broadening. Nevertheless, these crystal linewidths are considerably more than the linewidths observed in the vapor phase and certainly more than the natural radiative widths. 

Callomon, Parkin and Lopez-Delgado 9> have studied the variation in line widths with increasing vibrational energy in the lowest singlet system of benzene in the vapor phase. They took as a lower limit of detectable diffuseness Av 0.17 cm-1, where Av is the spectral linewidth. More accurate estimates of the dif-... 

This description of the relative spectral linewidths of the lowest excited toi states applies to the whole family of aromatic hydrocarbons. It also applies to the manifold of triplet jui states. In the case of benzene, Burland, Castro and Robinson 24> and Burland and Castro 25> have used phosphorescence and delayed fluorescence excitation techniques, respectively, to measure the absorption spectrum of the lowest triplet state, 3Biu of ultrapure crystals at 4 K. The origin is located at 29647 cm-1. Unlike all the earlier studies on the lowest singlet triplet absorption spectrum, this was not an 02 perturbation experiment. Here widths of less than 3 cm-1 were obtained. This result should be compared with the much broader bands 150-1 observed for the suspected second triplet ZE i in 5 cm crystals of highly purified benzene 26>. The two triplet states are separated by 7300 cm"1. 

Very similar spectral results are obtained from pyrene in mixed crystals of biphenyl and fluorene at about 10 K 28>. For pyrene the energy gap between the 1B2u and 1Biu origins is approximately 2000 cm-1 in fluorene and 1700 cm-1 in biphenyl crystals. These values are less than for the corresponding gap of naphthalene. However, the increased number of normal coordinates can be expected to lead to a similar density of states, and in fact a range of spectral linewidths paralleling those obtained for naphthalene is recorded. 

The well known anomalous fluorescence from S2 has been interpreted in terms of a much slower radiationless transition out of S2 than Si, such that for Si the fluorescence lifetime is severely shortened relative to the radiative lifetime. The anomaly is related to the unusual energy disposition of the two lowest excited singlet states. Hochstrasser and Li wished to ascertain whether the spectral linewidths were consistent with this interpretation and also whether the Si linewidths of azulene-ds were narrowed in comparison, as theoretically predicted. Their results are listed in Table 1. The spectral resolution was claimed to be <0.15 cm-1 as linewidths in the S2 system corresponding to the observed fluorescence lifetime are of the order of 10-4 cm-1, the linewidths of 0.50 cm-1 measured must be considered crystal-imposed. It is assumed that the maximum crystal inhomogeneity contribution to the Si linewidth is similarly 0.50 cm-1. This leads to a line broadening due to rapid nonradiative electronic relaxation of 1.61 (-hs) and 1.27 (-da) cm-1 as compared to 0.64 cm-1 (-hs) determined by Rentzepis 50> from lifetime studies of azulene in benzene solution at 300 K. 

Most X-band EPR spectra of transition metals are recorded at low temperatures (4-lOOK) using high-purity quartz tubes (no paramagnetic impurities) with a sample volume of about 300 pL. The minimum concentration of the sample depends on the broadness of its spectrum. Because EPR spectra are recorded as a first derivative (see subsequent text), the relationship between concentration, signal amplitude and spectral linewidth can be approximated as... 

Figure 9.7. A. Effect of MAS spinning speed on the spectral linewidth of the spatially dilute compound fluorohydroxyapatite (FAP) and the more concentrated fluorides NaF and CaF2- B. F MAS NMR spectra of a binary FAP and CaF2 mixture showing acceptable resolution of the 2 phases at spinning speeds which are sufficiently fast to narrow the Cap2 signal. From Kreinbrink et al. (1990), by permission of the copyright owner.

Table 19.3 Examples of human in vivo 19F relaxation times. While T2 relaxation times are relatively consistent, in vivo T, values (e.g., for fluoxetine and FBAL) vary considerably, indicating the difficulty of implementing a robust T1 measurement method with low signal levels and broad spectral linewidths... 

First, either a Lorentzian or Gaussian filter is applied to the FID to reduce the amount of noise. The choice of lineshape will depend on the shape of the frequency domain spectrum, the lineshape is related to how the fluorine spins interact with their environment. The filter linewidth is generally similar to or slightly less than the T2 value (T2 can be estimated from the spectral linewidth). After application of the time domain filter, a fast Fourier transform (FFT) is performed. The resultant frequency domain spectrum will then need to undergo phase adjustment to obtain a pure absorption spectrum. The amount of receiver dead time (time lost between the end of the excitation pulse and the first useful detection time point) will determine the presence and extent of baseline artifact present as well as how difficult phase adjustment will be to accomplish. 

Complexes of MV+- radical cations included in cyclodextrin (CDx) were observed both in methanol/aqueous solutions and as microcrystalline powder.21 In the former situation, the spectral linewidth did not decrease monotonically with temperature, as is the case in the absence of CDx. The linewidth decrease... 

ESR studies of pristine poly-[l,6-bls(N-carba2olyl)-2,4-hexadlyne](poly-DCH), a member of the general class of materials known as polydlacetylene, of the reaction of poly-DCH with bromine, and of poly-DCHBr, are reported and compared to previously reported ESR studies on similar systems. The ESR studies include measurements of the spectral linewidths, the g-tensors and the relative ESR signal intensity as a function of temperature for poly-DCH and poly-DCHBr,. Briefly, for pristine poly-DCH, two superimposed ESR spectra are observed. The spectral linewidths and g-tensors are Independent of temperature. In contrast, the ESR signal intensity is thermally activated and displays two activation energies. The kinetics of the disappearance of the original ESR spectrum observed in pristine poly-DCH and its replacement with a different ESR spectral envelope is presented as are the kinetic parameters which describe the reaction of poly-DCH with bromine. 

Spin Concentration Measurements, g-Values and Spectral Linewidths... 

Spin concentrations, g-valties and spectral linewidths have been measured for each of the samples studied. The results are summarized in Tables I and II. 

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