Electronic stopping power of antiprotons in transition metals

The electronic stopping power of charged particles is a key parameter describing their slowing down, energy transfer, and penetration range in matter [1]. It plays a crucial role in diverse fields, including nuclear reactor design, ion beam analysis, ion implantation, radiation damage studies, molecular fragmentation, and hadron therapy. Particularly, the antiproton stopping power provides a stringent test for theoretical models operating under charge conjugation symmetry. The difference between proton and antiproton stopping powers, known as the Barkas effect, remains an active topic of research and discussion [2]. In this work, we present a non-perturbative model to describe the stopping power of transition metals (Ni, Cu, Ag, and Au) for low-energy antiprotons, based on the momentum distribution function of the target’s valence and subvalence electrons, combined with a fully relativistic solution of the electronic wave functions for transition metals with Z > 40. The model’s predictions are compared with available experimental data [3], revealing the expected linear dependence on impact velocity and reproducing the characteristic differences between proton and antiproton interactions.

[1] P. Sigmund, Particle Penetration and Radiation Effects Vol. 1, Springer-Verlag, Berlin, (2006).

[2] G. Massillon-JL et al., Phys. Rev. Lett 134, 076401 (2025).

[3] S. P. Møller et al., Phys. Rev. Lett 88, 193201 (2002).