Energy Straggling of Heavy Charged Particles in Thick Absorbers

The theory of energy straggling attempts to calculate $F(E, S)$, where $F(E, S)dE$ is the fraction of the heavy charged particles which have an energy between $E$ and $E+dE$ after a path length $S$ has been traversed in absorbing medium. This paper develops a method of calculating $F(E, S)$ for path lengths large enough so that $F(E, S)$ is almost Gaussian. The method remains valid until a large fraction of the particles run out of energy. The theory is applied to calculations of $F(E, S)$ for 50-MeV protons in Be and for 5.3-MeV $\alpha$ particles in air. The calculations for $\alpha$ particles in air are in good agreement with the experimental results of Rotondi and Gieger. The theory is also in agreement with numberical calculations by Tschalär.