Diffusion-recombination stage

Here e denotes the intrablob electron, and r and r are solvation times of e and ec f, respectively. T r is the ion-molecule reaction rate of the radical-cation RH+1 ie j ep i kes, kps and kis are recombination and capture rate constants. 

In some cases when electron trapping leads to formation of the weakly bound state, S- (it may also takes place in reaction with hot electrons), reaction e+ +S — Ps becomes possible and should be taken into account. On the contrary, in the case of a strongly bound electron and sufficient affinity of S to the positron, this reaction may lead to e+S complex formation and, therefore, decreased Ps yield. 

The blob model describes reactions (16) in terms of nonhomogeneous kinetics via Eqs. (17-18) on concentrations of the particles. It is an adequate approach to the problem because the number of particles involved is large and local motion of the intrablob electrons and the positron is fast 

Here ct, ce and cp are the concentrations of the positive ions, electrons and the positron probability density at a point r measured from the center of the blob at time t. Dp is the diffusion coefficient of the positron, Di = De = Damb 0 is the ambipolar diffusion coefficient of the blob, a2 o2 ss a2 is the dispersion of the intrablob species, and a2 is the dispersion of the positron space distribution by the end of its thermalization. Decay rate Te-1 = 1/t + kescs is the sum of the electron solvation rate and possible capture by solute molecules t 2 = 1 /t2 + l/r + kpscs accounts for the free e+ annihilation, solvation and reaction with S. Similarly, t 1 = l/rjmr + hscs, where T r is the rate of the ion-molecule reaction. 

To calculate qf-Ps formation probability, Pps, we must integrate the term kepcecp over whole space and time  

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Principles and Applications of Positron and Positronium Chemistry 5.5.2 Diffusion-recombination stage... 

Considering the diffusion-recombination stage below, we neglect an interaction between the thermalized positron and its blob. This approximation, as we discussed above, assumes that the appearance of a positive potential in the blob, caused by outdiffusion of electrons, is nearly cancelled by the negative potential caused by e+ screening inside the blob. In this case we can apply the prescribed diffusion method to obtain the solution of Eq. (17). Let us write Cj(r,t) in the following form ... 

At the initial stage of reactions, the produced intermediate species such as the cation radical and the electron exist in a narrow space, the so-called spur. After the electron thermalization process, a pair of a cation radical and a thermalized electron remain in a spur. The geminate ion recombination of the cation radical and the electron occurs before these ionic species diffuse and spread uniformly in the media. Therefore the geminate ion recombination takes place in the spur. On the condition of a so-called single pair model,... 

Since the complications due to solvent structure have already been discussed, the remainder of this chapter is mainly devoted to a discussion of the complications introduced into the theory of reaction rates when the collision of solvent molecules does not lead to a complete loss of memory of the molecules about their former velocity. Nevertheless, while such effects are undoubtedly important over some time scale, the differences noted by Kapral and co-workers [37, 285, 286] between the rate kernel for reaction estimated from the diffusion and reaction Green s function and their extended analysis were rather small over times of 10 ps or more (see Chap. 8, Sect. 3.3 and Fig. 40). At this stage, it is a moot point whether the correlation of solvent velocity before collision with that after collision has a significant and experimentally measurable effect on the rate of reaction. The time scale of the loss of velocity correlation is typically less than 1 ps, while even rapid recombination of radicals formed in close proximity to each other occurs over times of 10 ps or more (see Chap. 6, Sect. 3.3). 

Until the geminate pairs start to mix, i.e., at relatively short times r relative diffusion coefficient, the monomolecular kinetics reads n(t) = n(0)u>(t), with n(0) = nA(0) = ne(0) being initial particle concentration. The distinctive feature of this stage is the linearity of the recombination kinetics n(t) with respect to the irradiation dose n(0). 

A comparison of the time developments of Y(r, t) in two limiting cases (pure contact reaction and strong tunnelling recombination) demonstrates their qualitative difference. In the latter case, the first stage is very short and is finished already at t a(R) x the further change of Y(r,t) is defined here entirely by the non-stationary diffusion. The relevant reaction rate for... 

Therefore, equation (4.2.21) with the substitution of for R cannot describe correctly the process of the steady-state formation if the diffusion process is controlled by the strong tunnelling (x 3> 1). In other words, strong tunnelling could be described in terms of the effective recombination radius i eff analogous to the black sphere in the steady-state reaction stage only. 

Another distinctive feature of strong tunnelling recombination could be seen after a step-like (sudden) increase (decrease) of temperature (or diffusion coefficient - see equation (4.2.20)) when the steady-state profile has already been reached. Such mobility stimulation leads to the prolonged transient stage from one steady-state y(r,T ) to another y(r,T2), corresponding to the diffusion coefficients D(T ) and >(72) respectively. This process is shown schematicaly in Fig. 4.2 by a broken curve. It should be stressed that if tunnelling recombination is not involved, there is no transient stage at all since the relevant steady state profile y(r) — 1 - R/r, equation (4.1.62), doesn t depend on >( ). 

Fig. 4.21. The computer simulation [102] demonstrating how the temperature stimulation affects the initial stage of the diffusion-controlled tunnelling luminescence. The cases a, b, c, correspond to three subsequent moments ti < 2 < h of the switching-on the stimulation (diffusion). The dashed lines are corresponding I(t) for the quasi-stationary recombination, provided the defect concentration changes negligibly.

To determine the relative abundance of ionization stages, there are no alternatives to spectroscopic measurements. In fusion devices, the distribution of the ionization stages deviates from coronal equilibrium, due to transport and finite confinement of the ions as well as charge exchange recombination with neutral hydrogen. Both the particle transport and the diffusion reduce the... 

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