Bohr's stopping-power formula derived for a classical free-electron gas

Abstract

Bohr's centenary stopping-power formula is rederived for a free electron gas (FEG) system within the framework of nonrelativistic classical mechanics. A simple and more concise expression for the stopping power of charged particles in FEG is demonstrated on classical grounds. Using semiclassical arguments and the Euler-Maclaurin well-known mathematical formula, Bloch's correction that links Bethe's quantum theory to Bohr's classical model is also recovered. The proposed semiclassical stopping-power formula contains the main physical ingredients for a general stopping formula applicable for different systems and energies and facilitates computational calculations.