Height and position of the Bragg peak in the stopping of charged particles

We have explored the systematics of the magnitude and location of the Bragg peak in the stopping of ions in matter in terms of the atomic numbers $Z1$ and $Z2$ of the projectile and target species, respectively. Extensive analysis of experimental results reveals major deviations from predictions by the Bethe stopping theory. In particular, the height of the Bragg peak follows a $∝Z14/3$ dependence rather than $∝Z12$ following from the Bethe theory. We assert this to be due to the fact that, with the exception of H ions, the Bragg peak lies below the energy range where the Bethe theory can be expected to be valid. Although experimental values from different sources show significant scatter, especially in the location of the peak on the energy axis, general trends are well described by the Bohr stopping theory. Moreover, good agreement is found in the absolute magnitude with computations with PASS, including oscillations as a function of $Z2$⁠, which are known to be related to the mean excitation energy or $I$-value.