The Role of Electron Capture and Energy Exchange of Positively Charged Particles Passing Through Matter

The conventional treatment of the Bethe-Bloch equation for protons accounts for electron capture at the end of the projectile track by the small Barkas correction. This is only a possible way for protons, whereas for light and heavier charged nuclei the exchange of energy and charge along the track has to be accounted for by regarding the projectile charge q as a function of the residual energy. This leads to a significant modification of the Bethe-Bloch equation, otherwise the range in a medium is incorrectly determined. The linear energy transfer (LET) in the Bragg peak domain and at the distal end is significantly influenced by the electron capture: Thus the stepwise filling operation of the electron shells along the particle track is treated by the Fermi energy EF of Fermi-Dirac statistics and leads to the conversion of carbon ions from C6+ at the beginning of the track to C1+ at the Bragg peak region. A rather significant consequence is that in the domain of the Bragg peak the superiority of carbon ions is reduced compared to protons.