Positron spur

Extending such calculations to the positron spur introduces additional difficulties, for two main reasons (i) even excepting solutes, one has to deal with a multicomponent inhomogeneous system (at least, e+, e and hole) (ii) much less is known on the properties of e+ than of e. At present, only one paper on Monte Carlo calculations on Ps formation has appeared [28]. 

The last exponential factor takes into account a possibility of the free-positron annihilation occuring during the Ps formation time, ips (on the order of some picoseconds) with the annihilation rate 1/t2 (< 2 ns-1). Obviously, the contribution from this factor is negligible. In nonpolar molecular media at room temperature rc is 300 A. Typical thermalization lengths b of electrons are < 100 A. Thus, the Onsager factor, 1 — err, is also very close to unity. Therefore, to explain observable values of Ps yields, which never exceed 0.7, we must conclude according to Eq. (11) that the terminal positron spur contains on average 2 to 3 ion-electron pairs. 

Therefore, it is difficult to justify the approach [25] to the Ps formation process where the end part of the e+ track is simulated by a straight-line sequence of isolated ion-electron pairs separated by more than 100 A. However, having considered the data for more than 50 liquids, the authors [25] came to the conclusion that multiparticle effects in the terminal positron spur are important for correct description of the intratrack processes. 

Inhibition or the reduction in the o-Ps yield is most probaly due to the inhibiting species scavaning precursors of Ps such as electrons and/or hot Ps atoms in the terminal positron spur [80], It is also found that the inhibition effect is dependent on the concentration of the inhibiting species. Figure 10.7 shows the dependence of the o-Ps intensity (I3) versus the concentration of a dopping chromophore in a PMMA polymer at two temperatures. With increasing amounts of the chormophore there is a decrease in the I3 value. This data can be fitted with the following relationship [42] ... 

A second model for Ps formation which has been recently suggested by Mogensen et al. (36) is the spur reaction model. They assume that Ps is formed as a result of a spur reaction between the positron and a secondary electron in the positron spur (Fig. 6). In this model a correlation should exist between the Ps formation probability and the availability of the electrons in the spur, that is to say that Ps formation must compete with electron - ion recombination and with electron and positron scavenging by the surrounding molecules, as well as with other processes. 

As can be seen in Figure 9.9b, the temperature dependence of (3 for PVA is similar to that of polyethylene (Matsuo et al. 2002). It can be seen that increases as a function of temperature up to -10°C. The increase in has been proved to be due to the positron irradiation effect on a polymer at low temperature. The secondary electrons that escape from the positron spur could be easily trapped in shallow potentials formed between the polymer chains when the motions of the molecular chains and groups are frozen at low temperature. Due to the positron irradiation time (experimental time), the probability of formation would become larger. As can be seen in this figure, becomes a maximum at around -10°C, and begins to decrease with increasing temperature. (3 attains a minimum at ca. 75°C and increases again beyond ca. 75°C. This is due to an apparent increase in the number of holes detected by positron annihilation, because of the thermal expansion of the holes at... 

A 1998 study using data from positron emission tomography or PET scans on humans also demonstrated that ketamine stimulates the release of dopamine, the brain s pleasure chemical. Most drugs of abuse spur the forced release of dopamine, reinforcing pleasurable associations in the user. 

Another model of positronium formation, the so-called spur model, was originally developed by Mogensen (1974) to describe positronium formation in liquids, but it has found some applications to dense gases. The basic premise of this model is that when the positron loses its last few hundred eV of kinetic energy, it creates a track, or so-called spur, in which it resides along with atoms and molecules (excited or otherwise), ions and electrons. The size of the spur is governed by the density and nature of the medium since these, loosely speaking, control the thermalization distances of the positron and the secondary electrons. It is clear that electrostatic attraction between the positron and electron(s) in the spur can result in positronium formation, which will be in competition with other processes such as ion-electron recombination, diffusion out of the spur and annihilation. 

A semi-quantitative picture of positronium formation in a spur in a dense gas was developed by Mogensen (1982) and Jacobsen (1984, 1986). If the separation of the positron from an electron is r, and there is assumed to be only one electron in the spur (a so-called single-pair spur), then the probability of positronium formation in the spur, in the absence of other competing processes, can be written as [1 — exp(—rc/r)] here rc is the critical, or Onsager, radius (Onsager, 1938), given for a medium of dielectric constant e by... 

The spur model, proven to be valid in condensed media, proposes that Ps formation would occur through the reaction of a (nearly) thermalized positron with one of the electrons released by ionization of the medium, at the end of the e+ track, in a small region containing a number of reactive labile species (electrons, holes, excited molecules) [1],... 

In spite of some important distinctions in the structure of the terminal positron blob and spurs, ionization columns and blobs of 5-electrons, where reactions of radiolytic hydrogen (H2) formation take place, these processes have much in common and it is natural to describe them in the framework... 

Radiation chemistry and Ps chemistry differ in the objects and processes they study. Being a probe of Ps chemistry, the positron delivers information about processes near and inside its terminal blob, while radiation chemistry primarily investigates the processes in isolated spurs. 

Nevertheless, it seems promising to investigate the problem of Ps formation jointly with the similar problem of intratrack radiolytic hydrogen formation. Despite some distinctions in conditions inside the terminal positron blob and spurs, blobs and ionization columns where reactions of formation of Ps and H2 occur, these processes have much in common. Their joint description diminishes uncertainty of the parameters involved in the model and leads to more reliable conclusions. 

The energetic positron slows down on its track to it s implantation depth, it ionizes the sample and leaves a spur of free electrons behind [27, 28]. The number of electrons at the terminal of the spur and their mobility determine the formation likelihood for positronium. The cross section for positronium formation becomes constant independent of incident energy. The second path to positronium formation is the 0re process [29]. When the potential energy needed to ionize an electron from a molecule is less than the binding... 

Performing an accurate dosimetry is a prerequisite of any radiolysis study. However, all standard chemical dosimetry methods cannot be used in nanoporous media, as they all rely on known radiolytic yields that are expected to be modified by confinement. An alternative would be to use Monte Carlo particle transport code (i.e. MNCP, EGS4, Geant, Penelope) that allows a calculation of the deposited dose. PENELOPE (Penetration and Energy Loss of Positrons and Electrons) has especially proven to be efficient in microdosimetric calculations.This code can treat electron propagation down to 100 eV, for any material. Therefore, these simulations cannot handle sub-nanometric pore and do not take into account the fact that for certain materials pore diameter is smaller than spurs and/or track size. For nanometric to micrometric pores, the approximation usually proposed is to correct the dose by the mean density of the system... 

There is competition for the free electrons between the positrons and the holes (OH radicals in the case of water media). When OH competes for these free electrons the addition of OH scavengers is predicted to cause an increase in the yield of o-Ps, a phenomenon called enhancement . On the other hand, addition of electron scavengers will reduce the yield of o-Ps, an effect known as inhibition . The yield of o-Ps is usually denoted by I3 (where and I2 are the yields of free positrons and />-Ps, respectively, having a much shorter half-life than o-Ps). Duplatre and coworkers - found that the yield of o-Ps in aqueous solution in the presence of concentration C of allylamine is given by equation 10. The enhancement factor 1 -h )SC is due to the reaction of allylamine with OH radicals, while the 1 + C inhibition factor is due to the reaction with aqueous or free electrons. The enhancement by amines is one of the main pieces of evidence for the existence of the spur mechanism . Yet, it should be emphasized that it does not rule out the simultaneous existence of both mechanisms . Duplatre and coworkers found that the inhibition by a strong inhibitor such as NO3 is the same in the presence or absence of allylamine. 

Figure 2. Schematic representation of the last spurs (shaded areas) in the tracks of (a) a positron or of Ps, and (b) of a muon or Mu, respectively (Reproduced with permission Adapted from [16] to take account of [15]). The signs denote the charges of the e and H20 primary ionization products.

The positronium formation probability Lq-ps is strongly reduced by the presence of electron acceptor groups in the polymer, since these groups trap free electrons that have been excited in the spur of the injected positrons, which otherwise could have formed positronium together with the positron [2, 4, 5]. 

In the case of implantation depths below approx. 50 nm, Iq.ps is reduced - the lower the positron implantation depth, the lower is Iq-ps- This reduction of io Ps can happen if fewer free electrons are available for the ortho-positronium formation. This is the case for the shorter spur of the positron due to a lower kinetic energy or if free electrons diffuse to the surface. Additionally, this Io.p reduction can be interpreted in terms of an out-diffusion of ortho-positronium [19]. In addition to these arguments, which are specific to the PALS method itself, depth-de-pendent properties in the top 10 nm of the epoxy, such as different densities of electron acceptor groups, could also play their part in the observed decHne in Io.ps. 

Equations (11. la)-(l l.ld) with ti = r ps, T2 = Te+ and T3 = ToPs present a rather naive picture of positron and Ps annihilation in polymers. Within the current ideas of Ps formation in polymers, the spur and blob models [Stepanov and Byakov, 2003], this picture remains valid when assuming that all intrablob positrons form Ps instantaneously in its final state (localized at its ground state in a hole) and that outside blob positrons do not take part in any reaction but annihilate with their characteristic lifetime re+. This general assumption seems not unreasonable since there are many (ca. 30) free electrons inside the blob but usually none outside. Trapped electron and positron states and their accumulation outside the blob during irradiation... 

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