Lifetime decay

Because the path of the s process is blocked by isotopes that undergo rapid beta decay, it cannot produce neutron-rich isotopes or elements beyond Bi, the heaviest stable element. These elements can be created by the r process, which is believed to occur in cataclysmic stellar explosions such as supemovae. In the r process the neutron flux is so high that the interaction hme between nuclei and neutrons is shorter that the beta decay lifetime of the isotopes of interest. The s process chain stops at the first unstable isotope of an element because there is time for the isotope to decay, forming a new element. In the r process, the reaction rate with neutrons is shorter than beta decay times and very neutron-rich and highly unstable isotopes are created that ultimately beta decay to form stable elements. The paths of the r process are shown in Fig. 2-3. The r process can produce neutron-rich isotopes such as Xe and Xe that cannot be reached in the s process chain (Fig. 2-3). 

The muon spin relaxation technique uses the implantation and subsequent decay of muons, n+, in matter. The muon has a polarized spin of 1/2 [22]. When implanted, the muons interact with the local magnetic field and decay (lifetime = 2.2 ps) by emitting a positron preferentially in the direction of polarization. Adequately positioned detectors are then used to determine the asymmetry of this decay as a function of time, A t). This function is thus dependant on the distribution of internal magnetic fields within a... 

Fig. 1.5. Paths of the r-, s- and p-processes in the neighbourhood of the tin isotopes. Numbers in the boxes give mass numbers and percentage abundance of the isotope for stable species, and /9-decay lifetimes for unstable ones. 116Sn is an s-only isotope, shielded from the r-process by 116Cd. After Clayton et al. (1961). Copyright by Academic Press, Inc. Courtesy Don Clayton.

Electron-density effects on fi-decay lifetimes also enable the total density to be placed in the range 2500 to 13 000 gm cm-3 all these parameters are characteristic of helium shell-burning zones as expected. 

Another large band-gap electron transport host is 3-phenyl-4-(l -naphthyl)-5-phenyl-1,2,4-triazole (TAZ), which has a HOMO (-6.6 eV) and LUMO (-2.6 eV). Using TAZ1 (109) as the host, a maximum EQE (ext) of 15.5% and a luminous power efficiency of 40 lm/W can be achieved in a phosphorescent OLED the value of phosphorescent decay lifetime of 7% Ir(ppy)3 in the TAZ (t-650 ns) is longer than that in CBP (t-380 ns) and the phosphorescence efficiency is approximately proportional to the excited state lifetime [174]. 

Figure 5.1. Representations of double-exponential and bimodal Lorentzian distribution analyses of DPH fluorescent decay lifetimes in liver microsomal membranes. Results (see Table 5.2) are normalized to the major component. The double-exponential analysis, represented by the vertical lines, recovers lifetimes near the centers of the Lorentzian distributions. The width of the distributions represents contributions from a variety of lifetimes. (From Ref. 17.)...

Table 5.2. Double-Exponential and Bimodal Lorentzian Analyses of DPH Fluorescence Decay Lifetimes in Liver Microsomes and Vesicles of Extracted Phospholipids"1 ...

In these Lorentzian lines, the parameter x describes the kinetic decay lifetime of the molecule. One says that the spectral lines have been lifetime or Heisenberg broadened by an amount proportional to l lx. The latter terminology arises because the finite lifetime of the molecular states can be viewed as producing, via the Heisenberg uncertainty relation AEAt > -h, states whose energy is "uncertain" to within an amount AE. 

While it is rather intuitive that the decay lifetime of a species is shortened by any quencher or scavenger, this simple concept is less than intuitive in the case of growing signals. Growth signals are observed whenever the product of reaction (even a transient product) is more strongly absorbing than its precursor. A typical case is... 

Supkowsky, R. M. Horrocks, de W. On the determination of the number of water molecules, q, coordinated to europium(IH) ions in solution from luminescence decay lifetimes. Inorg. Chim. Acta 2002, 340, 44-48. 

The first reasonably successful theory of diffusion-limited chemical reactions which specifically endeavoured to develop a model that could described, in principle, the competitive effect was introduced by Wilemski and Fixman [51], They considered the fluorescence of a species A which can be quenched by natural decay (lifetime t) and by a quencher, Q, of concentration [Q]... 

Rather than discuss the estimation of the density of the diffusing species around other species, it is perhaps of more interest to estimate the rate coefficient for a reaction, and certainly rather less complex than estimating the density. One of the first such studies was by Reck and Prager [507]. They considered the diffusion of the fluorophor in solution amongst an array of stationary quenchers. The fluorophor was excited at a constant rate F s-1 and the deactivation occurred by natural decay (lifetime r) and by contact quenching. This model is very similar to that chosen by Felderhof and Deutch [25] in their study of competitive effects. 

Figure 1. Orbital period of an electron moving in a Coulomb field, the time scales of some internal and external perturbations [3a-3d], and the observed (shorter, see below) lifetime for the polyatomic molecule known as BBC [4]. Note that at the highermost values of n the decay lifetime begins to shorten cf. Fig. 4.

Figure 4. The measured (shorter) decay lifetime (in nanoseconds) of dichloroanthracene (DCA) vs. the energy below the threshold to ionization. The curve is a fit for a diffusional motion of the electron about an anisotropic core in the presence of a weak (stray) DC field. For the derivation of the kinetic description from a Hamiltonian see Ref. 3c.

Laser beam expansion was also employed in LPA laser detection of HO (36-39). Hubler et al. (38) calculated an asymptotic laser-generated HO concentration in their quasi-continuous-wave expanded laser beam by assuming a chemical decay lifetime of 1 s for the excess HO. Chemical recycling of this HO was assumed to be slow with respect to the residence time of air in the laser beam. 

If the time scale of neutron capture reactions is very much less than 3 -decay lifetimes, then rapid neutron capture or the r process occurs. For r-process nucleosynthesis, one needs large neutron densities, 1028/m3, which lead to capture times of the order of fractions of a second. The astrophysical environment where such processes can occur is now thought to be in supernovas. In the r process, a large number of sequential captures will occur until the process is terminated by neutron emission or, in the case of the heavy elements, fission or (3-delayed fission. The lighter seed nuclei capture neutrons until they reach the point where (3 -decay lifetimes have... 

Two kinds of unimolecular decay lifetimes can be described. The first is the true radiative lifetime, i.e., the reciprocal of the rate constant for the disappearance of a species which decays only by fluorescence or phosphorescence. Since values of true fluorescence lifetimes may be calculated from the relationship between these quantities and the / numbers (vide supra) of the corresponding absorption bands, these values are (or at least approximations of them) are, in a sense, available. The second kind of lifetime is the reciprocal of an observed first order rate constant for decay of an excited state which may be destroyed by several competing first-order processes (some of which may be apparent first order) operating in parallel. We suggest that the two kinds of lifetime be distinguished by the systematic use of different symbols, as utilized by Pringsheim (4). 

Figure 7. Relative luminescence intensity and decay lifetime of Cu(I)Y during exposure to oxygen at 25°C and I atm. The decay times are average lifetimes except for the last point at which two distinct lifetimes, t = 28 /isec and r = 6 ysec (not shown here), were determined.

The total transition rate determines the measured decay lifetime,... 

Under these conditions, normal Stem-Volmer plots can be expected, both in terms of steady-state singlet-oxygen concentration and decay lifetimes. The slope of the Stem-Volmer plot (Ksy) is given by... 

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