Resonant exchange

Di Bari L, Kowalewski J and Bodenhausen G 1990 Magnetization transfer modes in scalar-coupled spin systems investigated by selective 2-dimensional nuclear magnetic resonance exchange experiments J. Chem. Rhys. 93 7698-705... 

Actually, the separation of donor and acceptor contributions to the electronic matrix element is not likely to be simple. One might define the resonance exchange reactions,... 

Figure 1. A schematic representation of a typical fluorescent-decay process illustrating the migration of energy by resonance exchange from ion to ion and its subsequent...

The nonradiative-exchange processes appear, at the moment, to be divisible into two groups (a) resonance exchange and (b) nonresonant phonon-assisted exchange. 

The process of nonradiative-resonance exchange has long been recognized to be of great importance in the understanding of luminescence. Numerous studies of the effect have been made. Of particular importance was the work by Dexter (41, 44), Dexter and Schulman (45), Forster (46, 47), and Perrin (48). The potential importance to rare earth-rare earth systems was stressed by Varsanyi and Dieke (49). 

In the nonradiative-resonance-exchange process an excited ion transfers its energy to a second ion without the emission of a photon, and with only a very minimal amount of energy lost to vibrations. For this process to occur, some coupling must, of course, exist between the ions. There is some evidence that this may be electrostatic (44,52). It appears that in most cases the ion-ion interaction is sufficiently weak that the energy levels of the rare earths are only slightly altered from their free ion positions. In this regard, one finds it convenient to talk about the system in terms of the states of the uncoupled ions. 

An alternate explanation of the emission intensities of terbium in the presence of other ions was given by Peterson and Bridenbaugh (54), that for europium was given by Axe and Weller (52). These authors point out that resonance exchange is a major factor in determining the emission intensities in these cases. This work has shed some doubt on the necessity of phonon-assisted transfer for the terbium and europium ions in the cases considered by Van Uitert and Iida. 

Johnson et al. (55) have reported a phonon-assisted energy exchange from trivalent erbium to trivalent thulium or to trivalent holmium. In this case, these authors were able to rule out resonance exchange completely Of some importance is that these systems are useful for laser oscillators, and the energy exchange results in a substantial decrease in threshold. 

The authors studied carefully the possibility of excitation of the 5Z)3 level after pumping the lattice band. They concluded that there was essentially none. The fact that the 5D4 level is selectively excited is quite interesting indeed. A resonance-exchange mechanism was postulated to explain this effect. 

The authors do not give a detailed explanation for the decreases in lifetime under paired dopings. There appear to be two possibilities, however. The first is changes in base-glass structure resulting in alterations of crystal field, and the second is resonance exchange between the ions. 

There is no question that certain ions are very effective in reducing the neodymium mean life. It appears possible to explain the decrease on the basis of resonance exchange between the neodymium and the quenching ions. 

The authors observe that other rare earths also quench terbium in the same solution. The quenching effects appear to correlate well with a resonance-exchange mechanism. This strongly points to the fact that the terbium-to-europium-transfer process is probably the same. Perhaps the most important aspect of this work is that it vividly shows that energy may migrate from one rare-earth ion to another without the necessity of a crystal or glass lattice. ... 

The most interesting aspect of this work is that the authors are able to rule out resonance exchange as the mechanism by which energy is transferred between the ions. They believe that transference takes place via phonon emission. It would be extremely interesting to determine the rates of ene/gy transfer between the ions, for this would then yield information concerning the rate of liberation of phonons. A study of the temperature... 

Fig. 32. The integrated intensity of magnetic reflections of x-ray resonant exchange scattering measured for NdNi2BjC and SmNi2B2C. Dashed line and full line model calculations for a magnetic moment parallel to the tetragonal a-axis and c-axis, respectively (after Detlefs et al. 1997b).

This formula was first derived in ref. 6 when calculating the kinetics of donor luminescence decay in the presence of the randomly, i.e. chaotically, located acceptors under the condition n N and on the assumption of the resonance exchange mechanism of energy transfer. Similar equations were later used for the analysis of experimental data on the kinetics of electron tunneling reactions obtained under conditions of the chaotic distribution of the reagents and at n < N. As a rule, only the first term of the exponent in eqn. (23) has been taken into account, which is equivalent to employing the previously mentioned (see Sect. 2.1) stepwise approximation of the function 0(R,t) = exp[- 1V(jR)(]. In this case, one obtains... 

Consider an excitation of the fast mode of one moiety of the dimer. The corresponding excited state is resonant with the state corresponding to the situation where it is the fast mode of the other moiety that is excited. A resonant exchange mechanism must occur when one of the fast modes has been excited. This mechanism, which is of a nonadiabatic nature, is at the origin of the Davydov coupling [74], which has been introduced by Marechal and Witkowski [18] in their pioneering works. 

Effective Hamiltonian involving Fermi resonance exchange and corresponding to the g part. 

Effective Hamiltonian involving Fermi resonance exchange of the g symmetrized part, when the g fast mode is in 1 )... 

There is indirect evidence from hydrogen maser studies [221] that the reactions H + H2, HD, D2 (v = 1) show a preference for resonant exchange reactions in the case of H + H2 (v = 1) and H + HD(i> = 1) and for non-resonant exchange for H + D2 (v = 1) in accord with theoretical calculations [222]. With recent experimental developments, particularly UV lasers, it can be expected that spectroscopic methods will be applied to measuring energy disposal for these reactions. 

The resonance exchange integral, Jbh(0) is indicated in Fig. 8.7. For the off-resonance exchange integral we take... 

Fig. 8.8. The dependence of resonance exchange integral on doping parameter...

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