Theory of Neutralization of an Isolated Ion Pair: Application of the Method of Prescribed Diffusion to Random Walk in a Coulomb Field

The problem of random walk of an ion pair in their mutual Coulomb field is formulated here in the framework of “prescribed diffusion.” The solution of this problem, when integrated over volume, gives the probability that the ion pair will remain unneutralized at a given time. In the limit t→∞, this probability calculated by the present method gives exactly the same expression as the Onsager formula. Half-life for neutralization is computed and its variation is studied with time, temperature and thermalization length. Case of an entire track is also discussed and possible application to neutralization of charges produced by ionizing radiations is indicated.