On the Theory of Energy Loss Distributions for Swift Charged Particles

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Abstract
There is a general integro-differential equation governing the change with penetration depth of the probability distribution in total energy loss of an energetic charged particle. A fundamental case belongs to small penetration depths where the total energy losses, in the main, are small compared to the energy of the particle. In the paper is introduced an internal variable, η, of the probability distribution, the variable being dependent on the distribution itself. The variable η suggests an exceedingly simple approximation procedure for finding the probability distribution in energy loss. Comparison with known solutions indicates that the errors of the first and second approximations are less than 10% and 2%, respectively. The method is applied to two modifications of the Landau distribution. It is shown that the Vavilov distributions have scaling properties, and the effect of atomic dipole resonances is estimated.

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