Classical-trajectory Monte Carlo calculations of the electronic stopping cross section for keV protons and antiprotons impinging on hydrogen atoms

Using the classical-trajectory Monte Carlo (CTMC) method, the electronic stopping cross sections of hydrogen atoms by protons and antiprotons impact are calculated. The results show that the CTMC method compares fairly well with previous quantum mechanics calculations of the stopping cross sections for the same colliding pairs. It turns out therefore that the CTMC method constitutes a reliable and, computationally speaking, convenient alternative to calculate the stopping of ions in matter. The present results also show that the stopping appears to be particularly sensitive to the angular momentum $\left(L\right)$ of the electron orbit. In the case of protons, the highest sensitivity to $L$ becomes evident around the energy of the maximum stopping. While for antiprotons the largest sensitivity of the stopping to $L$ is observed down at low bombarding energies, i.e., below 10 keV.

Figure 1

Stopping cross section for protons impinging on hydrogen. Symbols show the experimental data from Refs. 20 (×), 21 (엯), 22 (•), 23 (▴), and 24 (*). Lines are quantum-mechanics calculations after Schiwietz [15] (continuous) and Cabrera et al. [16] (dotted). The classical Bohr predictions [6] are plotted as a dashed line. Open squares indicate the results of the present CTMC calculations.

Figure 2

Stopping cross section for antiprotons $\left(\overline{p}\right)$ impinging on hydrogen. The continuous line shows experimental data for $\overline{p}$ on ${\mathrm{H}}_2$ in Ref. 25. The dotted line denotes the theoretical results for $\overline{p}$ on H from Ref. 26 and the dashed line shows the classical results of Bohr [6]. Full squares show the present CTMC calculations.

Figure 3

Fraction of the stopping for collisions that resulted in either ionization $(S_{ion}∕S_{tot})$, excitation $(S_{exc}∕S_{tot})$ of the target, or capture $(S_{cap}∕S_{tot})$ of the target electron by the projectile. Open symbols stand for protons that produced ionization (엯), capture (▿) and excitation (◻), whereas full symbols denote the cases of ionization (●) and excitation (▪) by antiprotons.

Figure 4

Influence of the eccentricities of the orbits in the initial distribution of the target electron upon the stopping cross section for (a) protons and (b) antiprotons impinging on hydrogen atoms.

Figure 5

Contribution to stopping from electrons initially orbiting around the target nucleus with an angular momentum $(L_n,d{L}_n)$, where $n=x,y,z$ [see Eq. (3)]. These results stand for (a) 80-keV protons and (b) 1-keV antiprotons and, in both cases, initial eccentricities are obtained using the procedure in Ref. 19.

Figure 6

Electron moving on orbit with a small eccentricity and a large, negative $L_z$.