Pair production length

The linear attenuation coefficient is the sum of the probabilities of interaction per unit path length by each of the three scattering and absorption processes photoelectric effect, Compton effect, and electron-positron pair production. The reciprocal of p is defined as the mean-free path, which is the average distance the photon travels in an absorber before an interaction takes place. 

Table 3.2. Properties of various g Ls mixtun s at atinosj)lieric pressure and 20°C for ininiimun ioni/ing particles. The radiation length A o is from reference [8]. The data on primary and total ion-pair production from a minimum ionizing particle is from [9] except for etliam, which is from (10], Other compilations appear in [10], [11], and [12]. Individual gas components and mixtures used in this study are shown.

Linear attenuation coefficient Probabilities per unit path length that the X-ray photon will be removed from the beam. This includes the effects of photoelectric absorption, Compton scatter, and pair production. 

The easiest way to proceed is to use vectors to describe this part of the problem. We represent the distance between the pair of scattering sites by the vector OP the length of which is simply r. To express di and d2 in terms of OP we construct the unit vectors a and b which are parallel to the incident and scattered directions, respectively. The projection of OP into direction a, given by the dot product of these two vectors, equals dj. Likewise, the projection of OP into direction b gives d2. Therefore we can write... 

Radiolytic ethylene destruction occurs with a yield of ca. 20 molecules consumed/100 e.v. (36, 48). Products containing up to six carbons account for ca. 60% of that amount, and can be ascribed to free radical reactions, molecular detachments, and low order ion-molecule reactions (32). This leaves only eight molecules/100 e.v. which may have formed ethylene polymer, corresponding to a chain length of only 2.1 molecules/ ion. Even if we assumed that ethylene destruction were entirely the result of ionic polymerization, only about five ethylene molecules would be involved per ion pair. The absence of ionic polymerization can also be demonstrated by the results of the gamma ray initiated polymerization of ethylene, whose kinetics can be completely explained on the basis of conventional free radical reactions and known rate constants for these processes (32). An increase above the expected rates occurs only at pressures in excess of ca. 20 atmospheres (10). The virtual absence of ionic polymerization can be regarded as one of the most surprising aspects of the radiation chemistry of ethylene. 

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