Electron escape probability

In the preceding part of this section, we have concentrated on the electron escape probability, which is an important quantity in the geminate phase of recombination, and can be experimentally observed. However, modern experimental techniques also give us a possibility to observe the time-resolved kinetics of geminate recombination in some systems. Theoretically, the decay of the geminate ion pairs can be described by the pair survival probability, W t), defined by Eq. (4). One method of calculating W t) is to solve the Smoluchowski equation [Eq. (2)] for w r,t) and, then, to integrate the solution over the space variable. Another method [4] is to directly solve Eq. (7) under relevant conditions. 

Figure 1 Electron escape probability as a function of the applied electric field. The solid lines are obtained from Eq. (23) for different values of the initial electron cation distance ro- The broken lines are calculated for ro = 1 nm from the numerical solution of Eq. (16) with the sink term given by k r) = A exp[—a(r—

An important result of the theoretical studies of the multipair effects is that the recombination kinetics in a cluster of ions, in which the initial separation between neighboring cations is 1 nm, is faster than the corresponding decay kinetics of a single ion pair [18]. Furthermore, the escape probability is lower than the Onsager value [Eq. (15)], and decreases with increasing number of ion pairs in the cluster (a relative decrease of about 30% for two ion pairs, and about 50% for five ion pairs). The average electron escape probability in radiation tracks obviously depends on the distribution of ionization events in the tracks, which is determined by the type of radiations and their energy. 

Fig. 5. Fitted electron escape probability and a (width of the Gaussian distance probability distribution for plotted as a function of the photon energies used to ionize water. The upper x-axis indicates the total excitation energy. Arrows indicate minimum possible values of escape probability or <7. [Reprinted from Ref. 49, Copyright 1996, with permission from American Chemical Society.]...

The reasons for the divergent effects of surface charge on TMB and ZnTPP photoionization yields in vesicular suspensions are unknown. Experimentally determined photoionization yields are complex quantities, which include as elementary processes primary ionization cross-section terms, dry electron escape probabilities, relatively complex electron hydration processes and recombination of various hy-... 

According to Onsager s theory the electron escape probability,

[Pg.1274]

This expression can be generalized in the presence of an external field, and the ratio of the escape probability as a negative ion to that as an electron in the absence of a scavenger computed as a function of the external field. From such an analysis and taking L = 4 A, a typical intermolecular separation, Mozumder and Tachiya obtained electron attachment cross sections in NP as 4 x 10-16,5 X 10 17, and 1 X 1CF18 cm2, respectively, for SF6, CC14, and CS2 with -15% uncertainty. 

FIGURE 9.1 Simplified derivation of Onsager s escape probability formula. In the stationary state a unit electron current at ro partitions as I toward the reaction radius and as Is toward the sink at infinity the latter is the escape probability. Reproduced from Mozumder (1969a), with the permission of John Wiley Sons, Inc. ... 

If an external field is present, the procedure would be the same except that now in place of 0(i) and (n) one would use the corresponding probabilities of electron escape as given by the Onsager equation in the presence of an external field (see Sect. 9.5). 

FIGURE 9.2 Variation of the ion escape probability in a nonpolar liquid with incident electron energy according to the simulations of Bartczak and Hummel. The curve shown is for exponential intra-ionic separation with a b value of 5.12 nm. (See the original reference for other parametric values.) Agreement with various limited experiments in n-hexane is only approximate. Reproduced from Bartczak and Hummel (1997), with the permission of Am. Chem. Soc . 

Here, Vd = pE is the drift velocity. The recombination and escape probabilities are now given by PR = NR /n+° L0 and Pkc = 1 - Pr. Since Vd = i, but T /r1 these probabilities are independent of mobility. However, the initial separation r0 is expected to depend (increase) with electron mobility, thus making the escape probability indirectly dependent on the mobility. These effects are quite similar to those in the Onsager theory... 

Detailed comparison of calculated and experimental results for the variation of the escape probability with the external field in Lar, LKr, and LXe has been made by Mozumder (1995a, b, 1996) using the data on LET, W value, mobility, and so forth. Experiments are with MeV electrons or beta-emitters having minimum LET in these liquids. The external field generally does not have any preferred direction relative to the track axis. Mozumder (1995a) argues that in such... 

FIGURE 9.4 Variation of the escape probability with the external field in LAr for a 1-MeV incident electron. Full curve, absolute calculation experimental points and calculated values normalized to 22 KV/cm are denoted by diamonds and circles, respectively. See text for explanation of parameter values used in the calculation. Reproduced from Mozumder, (1995a), with the permission of Elsevier . 

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