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Ion stopping force from Bohmian mechanics

P. L. Grande* and R. C. Fadanelli

F. Vuković, A. Niggas, and R. A. Wilhelm†

  • TU Wien, Institute of Applied Physics, Wiedner Hauptstrasse 8-10, 1040 Vienna, Austria

  • *Contact author: grande@if.ufrgs.br
  • †Contact author: wilhelm@iap.tuwien.ac.at
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Phys. Rev. Research 8, 013178 – Published 17 February, 2026

DOI: https://doi.org/10.1103/7plq-xskx

Abstract

We employed Bohmian mechanics to solve the equations of motion for a charged particle traveling in a free electron gas. Quantum effects are accounted for by including the Bohm quantum-mechanical potential Q, which depends on the electronic density, in the typical classical description. Our approach provides a computationally efficient alternative to traditional quantum calculations for determining the electronic stopping force of charged particles in matter. We use this framework to investigate the stopping of fast protons and slow highly charged xenon ions in the free electron gas. For highly charged ions, we predict the stopping force as a function of the projectile charge exchange.

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Phys. Rev. Research 8, 013178– Published 17 February, 2026
  • Received 20 May 2025
  • Revised 10 August 2025
  • Accepted 6 January 2026
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