Crossover decays

The 130 keV State. The decay of the 130 keV state has been studied extensively, and several inconsistencies are being resolved. The results of different measurements of the mean life and decay mode of the 130 keV state are discussed by Fink and Benczer-Koller (8). The half-life of the state has been measured electronically, and the transition matrix element for excitation has been derived from Coulomb excitation data (12). The combination of the Coulomb excitation yield, the internal conversion coefficient (8) a = 1.76 =t= 0.19, and the branching ratio (8) PCo = 0.060 zb 0.008 for the crossover decay to ground, yields a half-life ti/2 = (0.414 0.014) ns in excellent agreement with a recent (15) Mossbauer determination of the line width, r = (4.4 zb 0.4) mm/sec, equivalent to t1/2 = (0.49 0.05) ns. Wilenzick et al. (15) do not indicate the thickness of the Pt absorber used. 

Q = 7.275 MeV and Q = 11.16 MeV), when several a decays occur in sequence, the corresponding crossover decays can occur. For example, in the 4n chain the primary flow... 

The occurrence of nonradiative losses is classically illustrated in Figure 3. At sufficiently high temperature the emitting state relaxes to the ground state by the crossover at B of the two curves. In fact, for many broad-band emitting phosphors the temperature dependence of the nonradiative decay rate P is given bv equation 1 ... 

The best-studied system is Pb(CHj)4. This can easily be prepared using 22-yr Pb, which decays to °Bi by branched jS-emission—maximum j3-energies 15 keV (81%) and 61 keV (19%). The crossover y-transition is 14% converted. The results of various studies 22, 21) show retention of bonding in some 70-80% of the °Bi formed in the gas phase, and a similarly high yield in dilute solutions. Curiously, the yield of °Bi(CH3)4 fell to 18% at a mole fraction of 0.05 and rose again on further dilution (21). Adloff (2) has studied the f decay of PbPh4, with comparable results. 

Q-dependence of the plateau levels. The results for the model parameters are given in Table 3. The crossover time xe = 15 ns (T = 492 K) calculated with Eq. (41b) agrees well with the observed spectral shape in dividing the initial fast decay from the plateau-like behavior at longer times. Figure 25 (lower part) compares the experimental spectra for times longer than xe with the local... 

Q2 behavior takes place at decreasing Q. The position of the crossover point Q (c) is a direct measure of the dynamic correlation length (c) = 1/Q (c). The plateau value at low Q determines the collective diffusion coefficient Dc. A simultaneous fit of all low Q spectra where a simple exponential decay was found led to the concentration dependence and the numerical values of Dc... 

Deviations from the Forster decay (Eq. 9.29) arise from the geometrical restrictions. In the case of spheres, the restricted space results in a crossover from a three-dimensional Forster-type behavior to a time-independent limit. In an infinite cylinder, the cylindrical geometry leads to a crossover from a three-dimensional to a one-dimensional behavior. In both cases, the geometrical restriction induces a slower relaxation of the donor. 

Gutlich P, Goodwin HA (2004) Spin Crossover - An Overall Perspective. 233 1-47 Giitlich P (2004) Nuclear Decay Induced Excited Spin State Trapping (NIESST). 234 231—... 

A is generally positive and predicts (P/>P). B results from the shifts in internal force constants on condensation. An increased force constant on condensation leads in the direction of a normal VPIE, a decrease towards an inverse effect (P different temperature dependences. At low enough temperature A/T2 must predominate. The IE is normal and proportional to 1 /T2. At intermediate temperatures the B term, which can be positive, but more often is negative (see Section 5.4.1), may dominate. This accounts for the commonly observed crossover to inverse IE s. At higher temperatures yet, both terms decay to zero. The temperature dependence of VPIE can thus be complicated. 

Figure 3.8 Effects of tf-amphetamine on the wake EEG Mean EEG spectral values for six healthy male subjects who took placebo. 5 mg and 10 mg of d-amphetamine on separate occasions in a balanced crossover trial are shown Whereas the EEG trace 2 h after placebo (upper third) shows a rapid decline in alpha waves and an increase in theta waves (see arrows pointing to the alpha decrease and the theta increaee), the corresponding changes occurred later after 5 mg (middle third) andlOmg (tower third) d-amphetamine The decay of alpha and increaee of theta activities occurred after 2 mm on placebo, but only after 7 min on 5 mg d-amphetanine and after 12 mn on 10 mg of d-amphetamine, thus reflecting a vigilance-stabilizing effect of tf-aiphetamine (Matejcek, 1979, with permission)...

With the above boundary conditions, we can calculate a general surface mode of uniaxial gels. However, we restrict ourselves to a slowly diffusing mode (oc exp(— Dsk2t)) with its decay rate much smaller than the crossover frequency (oc given by Eq. (6.21). After some calculations, the diffusion constant Ds of this mode is obtained as [92]... 

Equation (2.1.84) predicts more slow decay as compared with the chemical kinetics (kinetic stage - (2.1.9)) unless d 2. That is, marginal dimension do = 2 occurs. The distinctive feature of (2.1.84) defining the range of its applicability is cofactor Sn2. Taking into account that (2.1.83) is valid as (d U where l = n(0) /d, the exponential kinetics (2.1.84) becomes essential as lD / n/(, l n = 8n ]/d. In another extreme case the preexponential factor predominates resulting in the asymptotics n (t) oc t d/4, as is observed for equal concentrations. That is, the crossover takes place (transition from power asymptotics to the exponential). Note that Schnorer, Sokolov and B lumen [48] have obtained these results employing the combination theory. 

Equation (2.43) describes a system that decays either by damped oscillations (when tjtls < 2A0) or by exponential relaxation (tjXLs > 2A0). Since riTLS grows with increasing temperature, there may be a crossover between these two regimes at /3 such that 2h xQ20J A0) coth(/3 /LA0/... 

In the superohmic case at 7 = 0, the system exhibits weakly damped coherent oscillations characterized by the damping coefficient rjTLS from (2.44), but with A0 replaced by Aeff. In the region lexponential decay, in accordance with our weak-coupling predictions. 

The corresponding correlation functions are sketched for characteristic temperatures in Fig. 9b. The critical temperature Tc marks the crossover from an ergodic state (liquid) to a nonergodic state (glass). In the liquid state, a two-step process describes the decay of the correlation function, where/is the fraction relaxed by the slow process (a-process) and 1 / is the part decaying due to the... 

Beyond the schematic picture sketched above, the two-step density correlation functions emerging from the idealized theory exhibit characteristic power-law decays toward and from the plateau /. Their experimental identification and analysis allows one to determine the crossover temperature... 

The asymptotic scaling laws of MCT describe the crossover from the fast relaxation to the onset of the slow relaxation (a-process)—that is, a power-law decay of 4>(f) toward the plateau with an exponent a, and another power-law decay away from the plateau with an exponent b. For the purpose of the present review, we again ignore the -dependence. 

While cooling, when the limit xa = 1 /, (cf. Eq. 15) is reached, the central Lorentzian NMR line, which is characteristic of a liquid (t-,8, solid-state spectrum, in the case of 2H NMR the Pake spectrum. The breadth of the solid-state spectra makes it difficult to measure the corresponding (short) free induction decay (FID), so that it is necessary to use echo-techniques (cf. Section II.D.2). Figure 38 (left) shows solid-echo 2H NMR spectra of glycerol-. The crossover from a Lorentzian line to the Pake spectrum is observed some 20% above Tg. Below Tg the spectrum is independent of temperature. In Fig. 37 (right), the corresponding 31P NMR spectra of m-tricresyl phosphate (m-TCP) are displayed. The characteristic spectral shape is now determined by the anisotropic chemical... 

Figure 48. Optical Kerr effect data for salol (top). Dashed line t l decay (bottom). Interpolation of the data by the universal p-correlator of MCT fixed by the exponent parameter X — 0.73. Inset Corresponding rectification plot yielding a crossover temperature 252 K (compiled from Ref. 70.)...

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