A stochastic formulation of site populations of heavy ions implanted in metals with related problems

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Abstract
In order to study the behaviour of transitions between sites of heavy ions implanted in metals we have developed a general stochastic treatment. The outcome is a partial differential equation for the generating function of probabilities of site population numbers for an N-site model. This equation is solved for the two-site case both with irradiation terms and without, the resulting probability distributions are compared and their corresponding mean values and variances calculated. The deviations from Poisson behaviour are pointed out. If the system is assumed to allow transitions in only one direction, then the resulting equations form a model of radioactive decay from which the conventional chain equations arise as the mean values. The corresponding probability distribution is shown to be Poisson when there is continuous irradiation and to remain Poisson when the irradiation ceases.

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