Comparison of the probability density functions for the ranges of electrons, positrons and protons

Abstract

The probability density functions Φ(ρz) for electrons, positrons and protons as well as for the ionizations [φ(ρz)] caused in the samples by the primary beams of the above mentioned particles have been studied. All of the dependencies obey Weibullean statistics. It has been shown that the probability density functions for the distribution of electrons as well as for positrons can be expanded from the conventional energy region of tens of keV to the region even closer to 1 MeV. The only difference is the disappearance of the surface charging in the high-energy region. A similar Φ(ρz) curve has been shown for the first time also for protons. The family of the ionization curves φ(ρz) seems to tend to be enveloped by the respective probability density curve Φ(ρz) for the distribution of the charged particle beam of the given energy. This has been shown for different tracers in a copper matrix.Given the probability density functions, one can easily select the correct solutions for the simulations of the particle beam attenuation in ambiguous situations; e.g., for 10 keV positrons penetrating a copper matrix it has been shown that the only proper energy-loss functions used in the simulations were those taking 11 and not 2 valence electrons into account.