Single-pair spurs

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 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. 

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. 

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,... 

In the second step, the thermalized electrons will either recombine with the ions in the track or spur or escape. The yield of free electrons is the integral of the product D r) x P(r) times the number of electron-ion pairs formed initially in the spur or track, Gtot, where P(r) is the probability of escape. For a single ion pair, P(r) is given by [5] ... 

Monotypic deciduous tree to 40 m leaves alternate or borne on spurs in clusters of 3-5 parallel veined, broad fan shaped, up to 12 cm, with notch at apex, forming two distinct lobes, hence the species name biloba . Flowers dioecious male flowers on pendulous catkins with numerous, loosely arranged anthers in stalked pairs on a slender axis female flowers are in pairs on long foot-stalks. The drupe-like fruits have an acrid, foul-smelling pulp (likened to dog droppings) surrounding a single smooth, oval, thin-shelled, semi-edible nut (seed). 

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