Coupled decay systems

The coupled Pb and U- Pb decay systems can provide age information based on Pb/ ° Pb and Pb/ Pb only. This is advantageous as Pb isotopic compositions can be determined with higher precision than the elemental parent/daughter ratio that must be applied in conventional chronological studies. This technique of Pb-Pb dating can provide the most precise absolute age data for solids formed early in the solar system and is the lynchpin for the calibration of extinct radioactive decay systems. Analytical improvements that have been achieved... 

In the previous section, we came to the conclusion a decay mechanism based on weak coupling to solvent modes is not likely to be a major contribution to the proton transfer rate even though it could potentially lead to the correct answer. We do stress here that the concept of rate actually means the velocity of a decay process to the final equilibrium state. In this section, we investigate a model that allows for strong coupling to vibrations, either in the molecule itself or in the environment, as that may be the dominant relaxation mechanism for decay. And we take the same approach that worked very well for similar classical systems we couple the system to a damped classical oscillator. 

It follows that there are two kinds of processes required for an arbitrary initial state to relax to an equilibrium state the diagonal elements must redistribute to a Boltzmaim distribution and the off-diagonal elements must decay to zero. The first of these processes is called population decay in two-level systems this time scale is called Ty The second of these processes is called dephasmg, or coherence decay in two-level systems there is a single time scale for this process called T. There is a well-known relationship in two level systems, valid for weak system-bath coupling, that... 

In addition to testing predictions of tire patlrway model in proteins, experiments have also examined tire prediction tlrat tire decay across a hydrogen bond (from heteroatom to heteroatom) should be about as costly as tire decay across two covalent bonds. Indeed, by syntlresizing a family of hydrogen bonded aird covalently bonded systems witlr equal bond counts (according to this recipe), it was demonstrated tlrat coupling across hydrogen bonded... 

Figure 1 Absorption spectra for system of excitons linear and locally coupled with strength S to nondispersive phonons with energy u>o calculated in NDCPA. B is excitonic bandwidth, and 7 is excitonic decay rate.

Coupling to these low-frequency modes (at n < 1) results in localization of the particle in one of the wells (symmetry breaking) at T = 0. This case, requiring special care, is of little importance for chemical systems. In the superohmic case at T = 0 the system reveals weakly damped coherent oscillations characterised by the damping coefficient tls (2-42) but with Aq replaced by A ft-If 1 < n < 2, then there is a cross-over from oscillations to exponential decay, in accordance with our weak-coupling predictions. In the subohmic case the system is completely localized in one of the wells at T = 0 and it exhibits exponential relaxation with the rate In k oc - hcoJksTY ". 

The preceding discussion was limited mostly to VP processes occurring by direct coupling of the quasibound state of the complex to the dissociative continuum, which is the simplest and most commonly observed decay route for the complexes. However, these systems also serve as ideal venues for studying an array of more complicated dynamical processes, including IVR, and electronic predissociation. This brief section will focus on the former, underscoring some of the inherent dynamical differences between Rg XY complexes by discussing the IVR behavior of a few systems. 

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