Annihilation shift

It was concluded from this and related works that suppression of the photodissolution of n-CdX anodes in aqueous systems by ions results primarily from specific adsorption of X at the electrode surface and concomitant shielding of the lattice ions from the solvent molecules, rather than from rapid annihilation of photogenerated holes. The prominent role of adsorbed species could be illustrated, by invoking thermodynamics, in the dramatic shift in CdX dissolution potentials for electrolytes containing sulfide ions. The standard potentials of the relevant reactions for CdS and CdSe, as well as of the sulfide oxidation, are compared as follows (vs. SCE) [68] ... 

Here /(R) and pflX) denote the shift and generalized momentum for the molecular vibration of the low frequency a>9 and reduced mass m, at the Rth site of the adsorbate lattice bi+(K) and K) are creation and annihilation operators for the collectivized mode of the adsorbate that is characterized by the squared frequency /2(K) = ml + d>, a,(K)/m , with O / iat(K) representing the Fourier component of the force constant function /jat(R). Shifts i//(R) for all molecules are assumed to be oriented in the same arbitrary direction specified by the unit vector e they are related to the corresponding normal coordinates, ue (K), and secondary quantization operators ... 

To invoke the perturbation theory for a small anharmonic coupling coefficient, we use the Wick theorem for the coupling of the creation and annihilation operators of low-frequency modes in expression (A3.19). Retaining the terms of the orders y and y2, we are led to the following expressions for the shift AQ and the width 2T of the high-frequency vibration spectral line 184... 

Temporal characteristics at early stages were elucidated by measuring fluorescence intensity with the gate time of 1.74 ns as a function of the delay time. Compared to the laser pulse, the time where the maximum intensity is attained shifts to the early stage as the laser fluence becomes high. Of course, we could not find out any decay component with intrinsic fluorescence lifetime of 17 and 35 ns. It is concluded that an Si - Si annihilation occurs quite efficiently during the pulse width. 

These traps, (Fig. 6) and similar effects in the motion of holes and other charges through polymers, would eventually be correlated also with such structural probes as positron lifetimes in macromolecular solids. Extensive recent studies of positron lifetime are based on positronium decay. In this, the lifetime of o-positronium (bound positron-electron pair with total spin one) is reduced from about 140 nanoseconds to a few nanoseconds by "pick-off annihilation" in which some unpaired electron spins in the medium cause conversion quenching of orthopositronium to para-positronium. The speed of the t2 effect is supposed, among other things, to represent by pick-off annihilation the presence of defects in the crystalline lattice. In any case, what amounts to empty space between molecules can then be occupied by orthopositronium.(14,15,16) It is now found in linear polyethylene, by T. T. Wang and his co-workers of Bell Laboratories(17) that there is marked shift in positron lifetimes over the temperature range of 80°K to 300°K. For... 

It is interesting to compare the properties of positive electrons, positrons, with the properties of electrons in nonpolar liquids. Values of the mobility of positrons, )x +, are now available for a few liquids. Early measurements for in -hexane ranged from 8.5 to 100 cm /Vs [181,182]. In a recent study, the Doppler shift in energy of the 511-keV annihilation gamma ray in an electric field was utilized to measure the drift velocity. This method led to fi+ = 53 cm /Vs in -hexane and 69 cm /Vs in 2,2,4-trimethylpentane [183]. Interestingly, these values are comparable to the mobilities of quasi-free electrons in nonpolar liquids. 

Only the value of the leading coefficient in the low energy expansion of the hadronic vacuum polarization is needed for calculation of the hadronic contribution to the Lamb shift (see the LHS of (3.32)). A model independent value of this coefficient may be obtained for the analysis of the experimental data on the low energy e+e annihilation. Respective contribution to the 15 Lamb shift [39] is —3.40(7) kHz. This value is compatible but more accurate than the result in (3.32). ... 

In a single sublattice crystal (A, B) with a fixed number of lattice sites and a negligible fraction of vacancies, the sum of the fluxes of A and B has to vanish if the number of sites is to be conserved. We just noted that if we formulate the A and B fluxes in the binary system as usual, they will not be equal in opposite directions because of the differing mobilities (bA 4= bB). However, if we have a local production (annihilation) of lattice sites which operates in such a way as to compensate for any differences in the two fluxes by the local lattice shift velocity, vL, we then obtain... 

Let us analyze these results one step further and ask about a quantitative measure of the Kirkendall effect. This effect had been detected by placing inert markers in the interdiffusion zone. Thus, the lattice shift was believed to be observable for an external observer. If we assume that Vm does not depend on concentration and local defect equilibrium is established, the lattice site number density remains constant during interdiffusion. Let us designate rv as the production (annihilation) rate of the vacancies. We can derive from cA+cB+cv = l/Vm and jA +/ B +./v = 0 that... 

Computer simulations [104, 105] of the evolution of interparticle distribution function (r, t) confirm validity of equation (5.3.9) derived for the A + A —> A reaction and demonstrate its discrepancy from the asymptotic distribution function for the similar (but not identical) annihilation reaction A + A — 0. The latter distribution function has its maximum shifted to the shorter distances and a longer tail at large distances. This distinction between two distributions is not very surprising since in the annihilation reaction we... 

A iV-electron vacancy (hole) in a shell may be denoted as nl N = ni4l+2-N (see aiso Chapters 9, 13 and 16). As we have seen in the second-quantization representation, symmetry between electrons and vacancies has deep meaning. Indeed, the electron annihilation operator at the same time is the vacancy creation operator and vice versa instead of particle representation hole (quasiparticle) representation may be used, etc. It is interesting to notice that the shift of energy of an electron A due to creation of a vacancy B l is approximately (usually with the accuracy of a few per cent) equal to the shift of the energy of an electron B due to creation of a vacancy A l, i.e. 

In this section we introduce three techniques frequently encountered in positron physics, namely those used to measure annihilation lifetimes and the Doppler broadening (or Doppler shift) and angular correlation of the annihilation radiation. These techniques, or variants thereof, are encountered throughout the rest of this work, and here we briefly describe... 

Additional, but rather less direct, evidence for the accuracy of the variational results for models H5 and H14 is provided by the excellent agreement between the theoretical and experimental lifetime spectra for positrons diffusing in helium gas, where calculation of the theoretical spectrum requires a knowledge of the momentum transfer and annihilation cross sections, both of which are derived from the wave functions generated in the calculations of the elastic scattering phase shifts. A detailed discussion of positron lifetime spectra is given in Chapter 6. 

An averaged value of cos 4> is dependent on the detection geometry) was used in evaluating AE1. A detailed analysis performed by Mills (1981) allowed for the fact that the Ps underwent acceleration for a significant proportion of its lifetime. From this he was able to deduce that the shifted annihilation line arose from a system with a mass-to-charge... 

Fig. 8.3. Annihilation gamma-ray spectra showing the blue-shifted photo-peak due to Ps- at various values of W, the acceleration potential. The arrows indicate the expected positions of these peaks. The 207Bi line (at approximately 569.6 keV) used for calibration is also shown. Reprinted from Positron Solid-State Physics, Proceedings of the International School of Physics Enrico Fermi , Course 83, Mills, Experimentation with low energy positron beams, 432-509, copyright 1983, with permission from Elsevier Science.

At the late stage of lamella orientation, classical topological defects (dislocations and disclinations) dominate [40, 41] (Fig. 8h and Fig. 9), and their movement and annihilation can be followed in Fig. 8h-i and Fig. 9. The latter presents an example of the apparent topological defect interactions and their transformations. Displayed are two dislocations of PMMA, which have an attractive interaction due to their opposite core sign. Therefore, in the next annealing step the dislocation is shifted... 

In Fig. 10, the transients exhibit quite different behavior from opal A to opal CT. In particular, a bi-exponential decay (Eq. 2) failed to reproduce the kinetics of opal CT. In this material, the emission is red-shifted towards 2.6 eV and the PL is strongly quenched at shorter time delays, with an unusual, non-linear kinetics in semi-log scale, indicating a complex decay channel either involving multi-exponential relaxation or exciton-exciton annihilations. Runge-Kutta integration of Eq. 5 seems to confirm the latter assumption with satisfactory reproduction of the observed decays. The lifetimes and annihilation rates are Tct = 9.3 ns, ta = 13.5 ns, 7ct o = 650 ps-1 and 7 0 = 241 ps-1, for opal CT and opal A, respectively. 

Bai et al. (2005) observed a phonon sideband with a frequency shift of 40-50 cm-1 located on the low-energy side of the 5Do <- 7Fo zero-phonon line (ZPL) in the 77 K excitation spectrum of Eu3+ Y203 NTs and NWs. However, vibronic sidebands generally appears at the high-energy side of the ZPL in the low-temperature excitation spectra since the vibronic transition involving the creation of a phonon with the annihilation of a photon is much more favored than the annihilation of a phonon at low temperature. The origin of this anomaly sideband remains unknown. 

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