Phonon-induced relaxation

In a recent paper Yen et al. (37) have considered experimentally and theoretically phonon-induced relaxation in the excited states of praseodymium in LaF3. This paper contains a very large number of references to the pertinent literature as applied to solids. 

The time-resolved solvation of s-tetrazine in propylene carbonate is studied by ultrafast transient hole burning. In agreement with mode-coupling theory, the temperature dependence of the average relaxation dme follows a power law in which the critical temperature and exponent are the same as in other relaxation experiments. Our recent theory for solvation by mechanical relaxation provides a unified and quantitative explanation of both the subpicosecond phonon-induced relaxation and the slower structural relaxation. 

Inoshita T. and Sakaki H. (1997), Density of states and phonon-induced relaxation of... 

Hochstrasser and Nyi in a study of vibrational energy redistribution after single vibronic level excitation in the S l -S o transition of azulene in naphthalene. In this system phonon-induced relaxation into host levels was mainly held responsible for vibrational relaxation. 

Fig. 76. Left Temperature dependence of the ZF muon spin relaxation rate in ErNis for the two crystal orientations indicated. The Curie temperature is 9.2 K. The solid line is a fit of rate to phonon induced relaxation (see text), Right Comparison of the 4f moment flucmation times in TmNij as seen by xSR (for two sample orientations) and Mfissbauer spectroscopy. The two data sets are simply normalized to each other (see text).

Yen, W.M., Scott, W.C., Schawlow, A.L., 1964. Phonon-induced relaxation in excited optical states of trivalent praseodymium in LaFs. Phys. Rev. 136 (lA), A271-A283. 

To conclude, regions B and C may show absorption-induced structures, especially thermally activated absorptions (hot bands). The diminution of this activated absorption causes the transition from region A to B in Fig. 2.9. Region B + C is a region of impurity, X-trap, or other spurious absorptions 41 it is unusable for quantitative analysis of the exciton phonon or polariton -phonon intrinsic relaxation mechanisms we investigate below. Therefore, our analysis will be concerned only with region A of the b- and a-polarized reflection spectra as the best candidates of a KK analysis. 

Another relaxation process involves the scattering of phonons from the excited state. These interactions do not remove energy from the excited state but serve to limit the coherence of the wavefunction resulting in a broadening of the state. The relaxation processes involve one or more phonons and are familiar to us from electron spin resonance (ESR) studies of the ground state of lanthanide compounds. These interactions have also been shown to be responsible for the thermal broadening of the spectra of trivalent lanthanides in crystals, see Di Bartolo (1968) and Hiifner (1978). These phonon induced effects are ultimately responsible for the thermalization of population of these systems. For a state that is metastable to a radiative process, the phonon relaxation processes vanish as... 

As discussed in Sect. 6.2, the electronic states of a paramagnetic ion are determined by the spin Hamiltonian, (6.1). At finite temperamres, the crystal field is modulated because of thermal oscillations of the ligands. This results in spin-lattice relaxation, i.e. transitions between the electronic eigenstates induced by interactions between the ionic spin and the phonons [10, 11, 31, 32]. The spin-lattice relaxation frequency increases with increasing temperature because of the temperature dependence of the population of the phonon states. For high-spin Fe ", the coupling between the spin and the lattice is weak because of the spherical symmetry of the ground state. This... 

When, however, phonons of appropriate energy are available, transitions between the various electronic states are induced (spin-lattice relaxation). If the relaxation rate is of the same order of magnitude as the magnetic hyperfine frequency, dephasing of the original coherently forward-scattered waves occurs and a breakdown of the quantum-beat pattern is observed in the NFS spectrum. 

We first consider the vibrational relaxation that can be induced by aijQqiqj (three-phonon processes) or Qq qi (four-phonon processes). In the three-phonon processes there are two accepting modes, while in the four-phonon processes there are three accepting modes. To calculate the rate of vibrational relaxation, we use... 

Finally, we would like to point out that in the off-resonance region, the response time of the nonlinearity is limited only by the optical pulse width r, as long as (Ea -Tiaj)/h >>2ir(x ). (8) This is no longer true when collisions (or phonons in solids) are present. For optical frequencies close enough to the absorption edge, the collision induced transitions to the excited state will cause the x s response time to be limited by the relaxation time of the excited states. (8)... 

A different view of the OMT process is that the molecule, M, is fully reduced, M , or oxidized, M+, during the tunneling process [25, 26, 92-95]. In this picture a fully relaxed ion is formed in the junction. The absorption of a phonon (the creation of a vibrational excitation) then induces the ion to decay back to the neutral molecule with emission (or absorption) of an electron - which then completes tunneling through the barrier. For simplicity, the reduction case will be discussed in detail however, the oxidation arguments are similar. A transition of the type M + e —> M is conventionally described as formation of an electron affinity level. The most commonly used measure of condensed-phase electron affinity is the halfwave reduction potential measured in non-aqueous solvents, Ey2. Often these values are tabulated relative to the saturated calomel electrode (SCE). In order to correlate OMTS data with electrochemical potentials, we need them referenced to an electron in the vacuum state. That is, we need the potential for the half reaction ... 

The presence of e-p coupling provides an additional channel for the relaxation of phonon states leading to an increase in phonon linewidths [13]. In addition, the modes shift in frequency due to the coupling. The magnitude of the induced shift A[Pg.341]

The first term is due to spontaneous radiative relaxation and nonradiative phonon relaxation as described in eq. (13), where / , is the probability of ion i in the excited state. The second term is due to energy transfer induced by ion-ion interaction, where W es and W A are rates of resonant and phonon-assistant energy transfer, which depend on distance between donor and acceptor RtJ. For resonant energy transfer... 

According to Meltzer s assumption, the faster relaxation in smaller nanocrystals embedded in glass is possibly due to stronger interaction of the electronic states of lanthanide ions with the larger density of low-frequency vibrational states in the glass, which may circumvent the slowing-down tendency of the relaxation induced by phonon confinement. 

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