The spur model

There are two models which utilize this mechanism, the spur model [18, 16] and the blob model (diffusion-recombination model) [19, 20]. In spite of the fact that both models answer the question about the Ps precursor in the same way, they differ as to what constitutes the terminal part of the e+ track and how to calculate the probability of the Ps formation. 

Quantitative formulation of the spur model was given by Tao [2l]. It is based on the following assumptions  

in the framework of the spur model, Ps formation probability is written as  

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. 

However, Eq. (11) apparently contradicts the correlation between experimentally measured Pps and the free-ion yields, /, at least in hydrocarbons (the higher the Pps the higher the G/i) [22]. 

---

For glutamic acid (18) and glycine (10) the yield of ammonia varies approximately as the cube root of the concentration. This variation agrees with the diffusion of the spur model which derives from the hypothesis that at higher solute concentrations, water radicals are scavenged which would react with each other in more dilute solution. However, for the effect of cathode rays on the aromatic amino acids phenylalanine, tryptophan, and tyrosine and for cystine, this relationship is inverted, and amino acid destruction decreased with an increase in concentration (29). 

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],... 

The spur model in polar solvents (Strasbourg Group) [2]... 

Enhancement of Ps formation. As expected from the spur model, all solutes that are efficient hole scavengers, thus somehow preventing the recombination process and increasing the electron availability (see reactions I—IX) enhance Ps formation. In water, strong positive ion scavengers are essentially the halide and pseudo-halide ions, together with amines. A convenient empirical equation to describe the Ps intensity variation is as follows [2] ... 

An explanation for the lost polarization in water was first introduced as part of the spur model of Mu formation and reactions as shown in Fig. 11 [63]. 

Here Mu is assumed to be formed as a result of combination of and an excess electron. This view is the same as for the spur model of positronium (Ps) formation. While the spur model has received strong support for positronium yield in condensed phases, the validity of the same model for Mu formation is not clear. Figure 11 presents the original form of the spur model of Mu formation, since it helps to contrast the difference between the epithermal model (Fig. 2) and the spur model of Mu formation. Alternatively, the part of Mu formation, i.e., p and excess electron combination, in Fig. 11 may be replaced with the picture of Mu... 

Fig. 11. A proposed scheme of Mu formation and reactions in water. Mu is formed by reaction with nearly thermalized p and an excess electron formed by radiolysis (the spur model of Mu formation) with the probability h, and the rest (Iiq) is solvated ttecomeing diamagnetic muon. Mu thus formed can further react with aqueous electrons by spin exchange reaction it is depolarized and the polarization is lost (Pi. By chemical reactions, a fraction of Mu is incorporated into diamagnetic muon while another fraction becomes dephased and forms a part of depending on how fast the reactions proceed. Mu that has not reacted is observed as free Mu (P )...

Four types of interaction between matter and radiation are under discussion - the photo effect, the Compton effect, the pair formation effect and the spurs model. In the following sections changes of the main food constituents (lipids, carbohydrates and proteins) will be summarized. 

Although the Ore model is more quantitative than the spur model, it works without serious errors only for gasses. In a condensed phase, conditions determining Ps formation are much more complicated. Usually, even some crucial parameters (e.g., ionization potential, solvating effect, etc.) are known with insufficient accuracy. Consequently, for condensed phases, one should use the spur model instead. Usually, it does not supply quantitative data, and its list of equations changes from material to material, hut, even so, its results are impressive. 

Independently of what one thinks of their formation mechanism, Ps atoms need space to be formed. In gasses, there is an enormous empty space between gas molecules, so space (or the shortage of it) is not a limiting factor of Ps formation. In fluids, however, Ps creates a small empty space, a bubble around itself. The bubble model was developed a long time ago (Ferrel 1957) and has been modified continually. Its present form tries to synthesize the results of the spur model and modern physical chemistry (Stepanov et al. 2000). In solids, structural free volumes might serve the empty space needed for positronium formation. 

The macroalkyl radicals are firstly trapped in solid polyethylene especially in crystalline phase. Then, allyl and polyenyl radicals are also partially screened toward subsequent reactions [99K2, 07B5]. The decay kinetics of radicals in irradiated polyethylene at room temperature and in vacuum follows the second order one, which is consistent with the spur model. 

---