The role of electron capture and energy exchange of positively charged particles passing through matter

TL;DR

This paper revises the Bethe-Bloch equation to better account for electron capture and energy exchange in charged particles, significantly affecting range calculations and the perceived advantage of carbon ions over protons.

Contribution

It introduces a modified Bethe-Bloch equation incorporating variable projectile charge to improve accuracy in energy loss and range predictions for various charged particles.

Findings

Electron capture significantly influences LET in the Bragg peak.

Modified equation alters the perceived superiority of carbon ions.

Range predictions are more accurate with the new model.

Abstract

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 LET in the Bragg peak domain and distal end is significantly influenced by the electron capture. A rather significant result is that in the domain of the Bragg peak the superiority of carbon ions is reduced compared to protons.