# A stochastic differential equation model for charged-particle straggling

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## Abstract

Considered in the present investigation is the energy loss due to charged particles that pass through an absorber. It is assumed that the rest mass of the charged particle is much greater than the rest mass of an electron and the energy of the charged particle is sufficiently high so that the particles do not capture electrons. With these assumptions, the charged particles lose energy by excitation and ionization with the absorber atoms. The mechanism of the energy loss is primarily the interaction of the Coulomb fields of the particles with those of the bound electrons in the absorber. If a charged particle passes through a target of given thickness, the particle will interact with the target's electrons. The charged particle will lose a certain amount of kinetic energy while passing through the target or stopping material. The amount of energy lost by this charged particle in the stopping material can be measured as the stopping power. A stochastic differential equation model is used to determine the amount of energy lost with respect to the distance traveled by the charged particle.