Bulletin of the Chemical Society of Japan
Online ISSN : 1348-0634
Print ISSN : 0009-2673
ISSN-L : 0009-2673
A Theoretical Consideration of the Electron-scavenging Process in Liquid Hydrocarbons. IV. Integral Transforms in the Prescribed Diffusion Approximation
Hideo YamazakiKyoji Shinsaka
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1973 Volume 46 Issue 9 Pages 2642-2646

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Abstract

The relations of the integral transforms and the integral form between various distribution functions have been discussed in the prescribed diffusion approximation for the Smoluchowski equation. The initial electron distribution from the central-ion cluster in a spur or a track, ω(r, 0); the time dependence of the central value of the electron distribution, ω(0, t); the time dependence of the space-averaged electron concentration, N(t), after pulse irradiation, and the scavenger-concentration dependence of the relative G-value of electron scavenging, Gs(ksCs), as a function of the scavenger concentration, Cs, and the rate constant, ks, are shown to be connected by this diagram of the Laplace transforms and the integral form:
(Remark: Graphics omitted.)
By the use of this relation, the various distribution functions are evaluated from the generalized Gaussian initial distribution. The square-root relationship of the Gs(ksCs) to the scavenger concentration is discussed.

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