Phonon creation

Fig. 9.34 Monitoring of inelastic excitations by nuclear resonant scattering. The sidebands of the excitation probability densities for phonon creation, S(E), and for annihilation, S —E), are related by the Boltzmann factor, i.e., S(—E) = S E) tTvp —Elk T). This imbalance, known as detailed balance, is an intrinsic feature of each NIS spectrum and allows the determination of the temperature T at which the spectrum was recorded...

Or is the frequency of the harmonic oscilator and b) are boson (phonon) creation (annihilation) operators. In order to use the perturbation theory we have to split the Hamiltonian (16) onto the unperturbed part Hq and the perturbation H ... 

Influence of Temporary Electron Trapping on Quasi-Elastic Scattering and Phonon Creation... 

If the free-atom recoil energy is much greater than the characteristic energy for phonon excitation ha>h where cor is the associated lattice vibration frequency, then phonon creation represents another mode of energy loss, which destroys resonance (29, 30, 32). For R° less than or of the order of tuo, a significant fraction of the nuclear events (emission and absorption)... 

For paramagnetic spin systems, there are two major processes of relaxation (55). One relaxation mode involves spin-flipping accompanied by lattice phonon creation and/or annihilation (spin-lattice relaxation), and the other mode is due to the mutual flipping of neighboring spins such that equilibrium between the spins is maintained (spin-spin relaxation). For the former mode of relaxation, th decreases with increasing temperature, and the latter relaxation mode, while in certain cases temperature dependent, becomes more important (th decreases) as the concentration of spins increases. 

If the exciton-phonon interaction Hep is strong compared to the emission probability, high-order terms in Hep contribute to P (2.131), providing strong luminescence at the expense of the one-phonon (Raman) process. In contrast, if the emission probability dominates the phonon creation probability, the peak (2.133) dominates the secondary emission at the expense of the luminescence.77 Examples of this competition will be discussed for the surface-state secondary emission, where the picosecond emission of the surface states, and its possible modulation, allow very illustrating insights into the competition of the various channels modulated by static or thermal disorder, or by interface effects. 

In the last subsection, we invoked phonons to explain the nonradiative broadening of the surface structures. However, at very low temperature, the surface state at the bottom of the excitonic band cannot undergo broadening either by phonon absorption or by phonon creation the phonon bath at 2 K does not suffice to account for the 3- to 4-cm 1 nonradiative width of the first surface resonance. Nevertheless, we assume the intrinsic nature of this broadening, since it is observed, constant, for all our best crystals.67120... 

The position and the width of this dip, at about I Ocm"1 above the Raman peak, indicate the energy gap above which the intrasurface relaxation, assisted by acoustical-phonon creation, competes with the surface-to-bulk relaxation. If we figure 3 to 4cm -1 for the relaxation rate to the bulk (for K 0 wave vectors cf. Section 1II.A.3), we conclude that the intrasurface relaxation, at 10cm 1 above the emitting state, is comparable. This conclusion on the acoustical-phonon relaxation is consistent with the theoretical estimates121127 (cf. Section III.A.4) and the experimental values derived by KK analysis of the bulk reflectivity (Section II.C.3b). 

For ZnO Ni the EA spectrum depicted in Fig. 6 (a) was measured at liquid-helium temperature T=4.2 K therefore, its vibrational part is shifled into the Stokes region of the spectrum and is associated with phonon creation. 

Here Efn(0) refers to the /th excited state of a free molecule in the crystal a n + (aQ is the Bose operator of creation (annihilation) of an intramolecular vibrational excitation in the nth molecule M2(k) refers to the energy of an optical phonon with the wave vector k connected with proton oscillations in the O H O bridge (bk) is the Bose operator of phonon creation (annihilation) and is the coupling energy between the molecular excitation and phonons. 

Let us consider an "impurity" atom moving in an atomic BEC. Atoms of another isotope or the same isotope but in a different internal (hyperfine) state can be viewed as impurities as long as their density is small enough not to modify considerably the BEC excitation spectrum. At "supercritical" velocities, namely, above the speed of sound in the BEC, the impurity atom is decelerated due to phonon creation in the BEC. The rate of such a process according to the standard Fermi golden rule (i.e., assuming exponential decay of the amplitude of the initial state) has been calculated for both a uniform BEC, [Timmermans... 

The interaction in non-metals (e.g. ionic crystals or covalent semiconductors) will be now expressed in terms of phonon creation ay and destruction a j operators related to the pnonon amplitudes in (2.2) by... 

Considering Equation 6.38 again, we need to transform the Hamiltonian expression. Thus, if cos(k) and ss(k) are the frequency and the polarization vector for the classic modes with polarization s and wave vector k, respectively, we can define the phonon creation (aks+) and annihilation ( /,s ) operators as... 

Expanding the quantity q in (3.90) with respect to deviations from equilibrium up to quadratic terms and introducing normal coordinates the Hamiltonian Hl can be written as a sum of Hamiltonians which correspond to harmonic oscillators in their normal coordinates. Then we use the phonon creation and annihilation operators, i.e. the operators 6 r and 5qr (q is the phonon wavevector and r indicates the corresponding frequency branch) and obtain the Hamiltonian Hl in the form... 

Suffice it to say that both Heff. (actually Hdd, Hdq as the case may be) and Heiec.- vibr. (a Hamiltonian describing vibronic coupling) must be included. Nevertheless, this type of energy transfer involving phonon creation and destruction at two sites where the oscillators are not originally coupled has been observed experimentally and occurs in many cases where energy transfer between excited and unexcited centers occurs. 

Here we use the convention that co > 0 for phonon annihilation and < 0 for phonon creation. For the differential reflection coefficient, or the fraction of incident atoms which are scattered into final solid angle dQf with energy Ef to Ef + dEf, the result from perturbation theory—as, for example, from the distorted wave Bom approximation [39, 41]—is that... 

The next phase for the theorists in connection with this work lies in predictions of helium atom scattering intensities associated with surface phonon creation and annihilation for each variety of vibrational motion. In trying to understand why certain vibrational modes in these similar materials appear so much more prominently in some salts than others, one is always led back to the guiding principle that the vibrational motion has to perturb the surface electronic structure so that the static atom-surface potential is modulated by the vibration. Although the polarizabilities of the ions may contribute far less to the overall binding energies of alkali halide crystals than the Coulombic forces do, they seem to play a critical role in the vibrational dynamics of these materials. 

Figure 45. TOF spectrum transformed to energy transfer distribution for CO/Rh(lll). The top panel shows the single-phonon creation and annihilation peaks for the fmstrated translational motion of CO at 5.75 meV along with a difiuse elastic peak at zero energy transfer. In the lower panel, the shift in energy to 5.44 meV due to the heavier mass of the C 0 isotope is clearly discernible (dashed vertical line). (Reproduced fiom Fig. 3 of Ref. 130, with permission.)...

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