Trajectory effects on the energy loss cross section in collisions of H$$^+$$ and He$$^{2+}$$ ions with atomic hydrogen

Abstract Energy loss processes are fundamental for designing particle detectors, improving radiation therapies, and understanding fundamental processes in materials science. This property is often calculated by assuming straight-line trajectories. While this constant-velocity approximation is valid at high collision energies, it does not satisfy energy conservation. In this work, we investigate these trajectory effects by solving the time-dependent Schrödinger equation in a numerical lattice, using both coupled electron-nuclear dynamics and the straight-line trajectory approximation. We study H $$^+$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mrow/> <mml:mo>+</mml:mo> </mml:mmultiscripts> </mml:math> and He $$^{2+}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mrow/> <mml:mrow> <mml:mn>2</mml:mn> <mml:mo>+</mml:mo> </mml:mrow> </mml:mmultiscripts> </mml:math> projectiles incident on atomic hydrogen over the energy range 0.1–900 keV/u. We confirm that the total charge exchange cross sections are trajectory-independent within the energy range considered and show good agreement with experimental and theoretical data. However, clear trajectory-dependent differences emerge at intermediate to low energies for projectile energy loss with the straight-line approximation underestimating it at low collision energies. At high collision energies, the electronic stopping cross sections are in excellent agreement with available theoretical data. We also show that charge exchange and energy loss are correlated below the stopping cross section maximum, exemplified by the resonant charge exchange in H $$^+$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mrow/> <mml:mo>+</mml:mo> </mml:mmultiscripts> </mml:math> +H collisions in contrast to the non resonant He $$^{2+}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mrow/> <mml:mrow> <mml:mn>2</mml:mn> <mml:mo>+</mml:mo> </mml:mrow> </mml:mmultiscripts> </mml:math> +H. Overall, our work highlights the importance of nuclear trajectory considerations in collision dynamics and offers a foundation for further investigations of more complex systems. Graphic abstract