Mean transition energy

The first moment. Mi, is equal to the mean transition energy  

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Fig. 2.2 Intensity distribution /( ) for the emission of y-rays with mean transition energy Eq. The Heisenberg natural line width of the distribution, F = S/t, is determined by the mean lifetime T of the excited state (e)...

Figure 11.9 An oscillating wavepacket leads to periodic variation in the mean transition energy between two electronic states (a) and thereby to an oscillatory shift of the spectrum (b). The amplitude of the oscillating signal is proportional to the slope of the spectrum.

Experimental values are shown in Figure 5.14(a). As could be expected, the stronger bound electrons in the closed-shell clusters have a higher mean resonance energy compared to the electrons in open-shell clusters of similar size. The mean transition energy is nearly independent of temperature as discussed below. 

Figure 5.15 shows the temperature dependence of three cluster properties averaged over the optical response. Plotted are (1) the mean transition energy Eq, see Eq. (10)), (2) the... 

Here /I " stands for the w element of the static /-order multiple polarizability of the solute. They can be computed via quantum mechanics, since it only requires the ground-state wavefunction of the solute [40]. The mean transition energies and can be related to ionization potentials of the partner... 

Figure 4.8 (a) Periodic variation of the mean transition energy between two electronic... 

Kaindl et al. [186] have plotted the isomer shift results for metallic hosts versus the number of outer electrons of the 3d, Ad, and 5d metals and found the transition energy to decrease when proceeding from a to a Ad and further to a 3d host metal in the same column of the periodic table. This systematic behavior is similar to that observed for isomer shifts of y-rays of Fe(14.4 keV) [193], Ru(90 keV), Pm (77 keV), and lr(73 keV) [194]. The changes of A(r ) = (r )e — (r )g for these Mossbauer isotopes are all reasonably well established. Kaindl et al. [186] have used these numbers to estimate, with certain assumptions, the A(r ) value for Ta (6.2 keV) and found a mean value of A(r ) = —5 10 fin with some 50% as an upper limit of error. The negative sign of A(r ) is in agreement with the observed variation of the isomer shift of LiTaOs, NaTaOs, and KTaOs, as well as with the isomer shift found for TaC [186]. 

Robinson and Frosch<84,133> have developed a theory in which the molecular environment is considered to provide many energy levels which can be in near resonance with the excited molecules. The environment can also serve as a perturbation, coupling with the electronic system of the excited molecule and providing a means of energy dissipation. This perturbation can mix the excited states through spin-orbit interaction. Their expression for the intercombinational radiationless transition probability is... 

Experimental data were taken from refs. 40-45 and theoretical data from ref. 6. Excitation energies of the La bands exhibit a significant correlation with N- Fj transition energies [E(N -> Vj)] and those of the Lb and Bb bands with the mean of the excitation energies of transitions l->2 and 2- -l, E(N-> V). In the case of the data on the La bands that are marked with footnote c in Table III, the correlation... 

The variation of fluorescence intensity with pH can provide direct information about the pfCa in the excited state. Forster suggested the following indirect procedure for estimating excited-state pfCa values for phenols. Let Ei represent the energy of the 0-0 transition (preferably measured as the mean of the observed 0-0 transition energies in absorption and fluorescent emission spectra) let E2 represent the energy of the... 

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