Multiple-pair spur

Second, the "satellite ions" could be generated in scavenging reactions of the solvent holes with radiolytic products in multiple-pair spurs [25,61-65]. The olefins are formed upon the fragmentation of excited solvent molecules generated in recombination of short-lived electron-hole pairs [1]... 

While being useful exercises, both of these simulations were based on simplified kinetic schemes and physical models of spur dynamics. For some problems (free ion yields) these considerations may be of little importance, for other (product yields) the oversimplification leads to ambiguous results. In particular, this applies to calculations of the "singlet yields" (implicitly identified with the yields of the lowest Si states) where the estimates entirely depend on the kinetic scheme [85,86]. Most of such calculations address only one facet of the problem the relative significance of "geminate" recombination and cross-recombination in multiple-pair spurs. In the recent Monte-Carlo simulations [85], the initial spatial distribution of ionization events was calculated using the same approach that was used in the calculations of the free ion yield (see above). The total yield of singlet recombination for the primary pairs was estimated. 

While it is an open question whether the quenching reactions in multiple-pair spurs and sensitization of solute fluorescence by "dark" states can explain the discrepancies, it seems more likely that the loss of the solute luminescence is due to some irregularity in the behavior of cyclohexane holes. One possibility is that rapid electron spin-relaxation in these holes randomizes [RH +A " geminate pairs and reduces the A yield (see section 2.2). The occurrence of such randomization does not contradict the experimental estimates of fg (0.5-0.6) for recombination of secondary pairs these estimates... 

The methods discussed so far are essentially limited to isolated ion-pairs or, in the admittedly crude approximation, to cases when a multiple ion-pair spur can be considered to be a collection of single ion-pairs. Additionally, it is difficult to include an external field, as that will destroy the spherical symmetry of the problem. Stochastic treatments can incorporate both multiple ion-pairs and the effects of an external field. 

In the ME model of recombination kinetics in a multiple ion-pair spur, the probability PN that N ion pairs will remain extant at time t is given by (Green and Pimblott, 1990)... 

Pimblott (1993) has used MC and ME methods for the external field (E) dependence of the escape probability (Pesc) for multiple ion-pair spurs. At low fields, Pesc increases linearly with E with a slope-to-intercept ratio (S/I) very similar to the isolated ion-pair case as given by Onsager (1938). Therefore, from the agreement of the experimental S/I with the Onsager value, one cannot conclude that only isolated ion-pairs are involved. However, the near equality of S/I is contingent on small Pesc, which is not expected at high fields. 

Dodelet and Freeman (1975) divide the geometry of a multiple-ion-pair spur into spherical concentric shells such that exactly one electron is contained in each shell with respect to the initial distribution/(r)—that is,... 

In Sect. 7.4.6, we discussed various stochastic simulation techniques that include the kinetics of recombination and free-ion yield in multiple ion-pair spurs. No further details will be presented here, but the results will be compared with available experiments. In so doing, we should remember that in the more comprehensive Monte Carlo simulations of Bartczak and Hummel (1986,1987, 1993,1997) Hummel and Bartczak, (1988) the recombination reaction is taken to be fully diffusion-controlled and that the diffusive free path distribution is frequently assumed to be rectangular, consistent with the diffusion coefficient, instead of a more realistic distribution. While the latter assumption can be justified on the basis of the central limit theorem, which guarantees a gaussian distribution for a large number of scatterings, the first assumption is only valid for low-mobility liquids. 

These results imply that the use of the representative single ion-pair distribution in the ionization produced by low-LET irradiation in liquid hydrocarbons can be approximately justified even though the track itself has considerable contribution from multiple-ion-pair spurs and short tracks. It also means that even in the case of an isolated ion-pair, the long-time limit of the existence probability is perturbed by the long-range coulombic field. 

In conclusion we may state that there is evidence for multiple ion-pair recombination in spurs yet a theoretical analysis of free-ion yield and scavenging at low-LET based on the geminate ion-pair picture is meaningful in view of the similarity of the recombination process in the geminate and multiple ion-pair cases. However, if this analogy holds, the geminate ionization yield has to be somewhat less than the true ionization yield. 

Two triplet correlated radical pairs The second type of action at a distance concerns type (2) spurs where a triplet encounter between 1,4 (which occurs in 75% of the cases in spurs) causes the disjoint pair 2,3 to adopt the same spin multiplicity. The normaUsed wavefunction after removing the singlet terms becomes... 

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