Oscillator strength spectra

Dipole oscillator strengths form important input into all stopping models based on Bethe or Bohr theory. Emphasis has frequently been on total /-values which show only little sensitivity to the specific input. More important are differential oscillator-strength spectra, in particular at projectile speeds where inner-shell excitation channels are closed. Spectra bundled into principal or subshells [60] are sufficient for many purposes, but the best available tabulations are based on analysis of optical data rather than on theory, and such data are unavailable for numerous elements and compounds [61]. 

Figure 13. Oscillator-strength spectra for photoabsorption of NH3 solid line, electron-impact32 absorption smooth curve through 400 data points, normalized to a total / value of 8 dashed curve, Metzger and Cook 124. Dashed-dotted curve, Sun and Weissler.125.

Figure 17. Oscillator-strength spectra for argon L-shell ionization, leading to charge states 1 to 4.149...

Figure 24. Oscillator-strength spectra for and H+ from reference.166 Open triangles are photoionization data due to Samson et al.169...

Figure 25. Carbon Af-shell oscillator-strength spectra of CO. In C+ spectrum (c) above 295 eV scale has been changed by a factor of 5.173...

Figure 21. Absorption oscillator-strength spectrum of H2 electron impact164 normalized on an integral value of 2 (TRK sum rule) with 1% correction for energies beyond 80 eV +, photoabsorption , data from Cook and Metzger 161 A> extrapolation of Generalized Oscillator Strength obtained at 461-eV impact energy.167...

Figure 4-2. INDO/SCI-siuiulaled linear absorption spectrum of the eleven-ring PPV oligomer. The vertical lines represent the oscillator strength of the transitions that are described the site labeling used tor the wavcluiiclion analyses is shown on lop.

Fig. 6. Optical spectrum of Ir atoms isolated in solid Ar at 10-12 K, compared to the gas-phase atomic transitions of Ir. The stick heights correspond to reported oscillator strengths of gaseous Ir atoms (49).

In Eq. (4.5) the donor emission spectrum/ and the acceptor absorption spectrum eA are separately normalized to unity, so that the transfer rate is independent of the oscillator strength of either transition. Unfortunately, the constants W and L are not easily determined by experiment. Nevertheless, an exponential dependence on the distance is expected. It should be noted that this type of transfer involves extensive orbital overlap and is guided by Wigner s (1927) spin rule. 

Certain features of light emission processes have been alluded to in Sect. 4.4.1. Fluorescence is light emission between states of the same multiplicity, whereas phosphorescence refers to emission between states of different multiplicities. The Franck-Condon principle governs the emission processes, as it does the absorption process. Vibrational overlap determines the relative intensities of different subbands. In the upper electronic state, one expects a quick relaxation and, therefore, a thermal population distribution, in the liquid phase and in gases at not too low a pressure. Because of the combination of the Franck-Condon principle and fast vibrational relaxation, the emission spectrum is always red-shifted. Therefore, oscillator strengths obtained from absorption are not too useful in determining the emission intensity. The theoretical radiative lifetime in terms of the Einstein coefficient, r = A-1, or (EA,)-1 if several lower states are involved,... 

FIGURE 6.2 Absorption spectrum of the hydrated electron. The spectrum is structureless, broad (half-width 0.84 eV), intense (oscillator strength 0.75), and has a single peak at 1.725 eV. (See text for details.)... 

The oscillator strength for absorption is a very important quantity signifying the nature of the transition. If the absorption spectrum is known, the oscillator strength can be calculated using Eq. (4.20). Instead of numerical integration, one often assumes that the spectrum is approximately gaussian with the same half-width Av (cm-1) as experimentally observed. One then obtains/, the oscillator strength, as... 

The excited state is formed out of a combination of 2p orbitals, and the absorption spectrum is seen as a Is-1 2p transition. The excited state is weakly bound in this model, by 0.9 eV. The calculated oscillator strength is too low, which seems to be a feature of all structural models. There is no configurational... 

Much worse than the oscillator strength is the line shape. The calculated absorption spectra has no similarity with what is experimentally seen. The calculated half-width is always smaller, typically by a factor of 2 the exact reasons for this are only speculated. It is common knowledge that a photodetachment process is capable of giving a very broad absorption spectrum, but a satisfactory method has not been developed to adopt this with the bound-bound transition of the semicontinuum models. Higher excited states (3p, 4p, etc.) have been proposed for the solvated electron, but they have never been identified in the absorption spectrum. 

We have selected several unblended CH lines located in the near-UV between 3145-3190 A modified their oscillator strengths (gf-values) by fitting the solar high-resolution spectrum and assuming solar abundance of carbon 8.56 from Anders and Grevesse (1989). These lines are measurable in dwarfs down to the metallicities —3. Our results are shown in the Fig. 1. We confirm the metallicity dependence of the C/O ratio (Tomkin et al. 1992, Akerman et al. 2004). On the other hand, our plot for C/O shows a steep rise at [0/H]< —1. It is not clear if this effect is real. The work is in progress to address this issue using other abundance indicators such as CH 4300 A and better quality spectra. 

It should be noted that no such difficulty appears with the integral of an absorption spectrum because the absorption coefficient is proportional to the logarithm of a ratio of intensities, so that e(A) = e(v). For instance, in the calculation of an oscillator strength (defined in Chapter 2), integration can be done either in the wavelength scale or in the wavenumber scale. 

Equation (4.79) shows that Ro, and consequently the transfer rate, is independent of the donor oscillator strength but depends on the acceptor oscillator strength and on the spectral overlap. Therefore, provided that the acceptor transition is allowed (spin conservation) and its absorption spectrum overlaps the donor fluorescence spectrum, the following types of energy transfer are possible ... 

It is difficult to measure the oscillator strengths of molecules embedded in a matrix. Despite this, good values of can be determined as a function of the temperature. A procedure we have used to extract the information from excitation spectra was to set the maximum of the excitation spectrum measured at room temperature equal to the extinction coefficient at the absorption maximum in solution. The integrals of the excitation spectra were then normalized to the integral of the corresponding spectmm at room temperature, which is reasonable because the oscillator strength / of a transition n <— m does not depend on the temperature. 

A detailed study of the electronic structure and optical properties was published for the spiro derivative of f-Bu-PBD, Spiro-PBD (40) [108]. The vibronic structure of the lowest energy absorption band is well resolved, in solution as well as in the amorphous him. The 0-0 transition is at 351 nm (3.53 eV), the 0-1 and 0-2 vibronic bands that have a higher oscillator strength, are at 336 nm (3.69 eV) and 318 nm (3.90 eV), respectively. The fluorescence spectrum of this compound is symmetrical to the absorption spectrum with a Stokes shift of 43 nm. 

The oscillator strengths were estimated from the spectrum given by Brouwer and collaborators (1965a) using the relationship/= 4-32 x 10 vx/j. 

Considering our single two energy level center, it is easy to understand that the area under the absorption spectrum, /a co) dco, must be proportional to both /x and the density of absorbing centers, N. In order to build up this proportionality relationship, it is very common to use a dimensionless quantity, called the oscillator strength, f. This magnitude has already been introduced in the previous chapter (Section 4.3), when treating the classical Lorentz oscillator. It is defined as follows ... 

EXAMPLE 5.4 Figure 5.8 shows the absorption spectrum of a NaCl crystal containing color centers generated by irradiation. The band peaking at 443 nm is related to the so-called F centers, for which the oscillator strength isf= 0.6. From this absorption band, determine the density of the F centers that have been produced by the irradiation process. Assume a refractive index of n = L6 for NaCl. 

Instead of one resonance frequency per individual electron, Bethe recovered the spectrum of resonance frequencies for the atom, weighted by dipole oscillator strengths satisfying the sum rule... 

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