Antiproton stopping in ${\text{H}}_2$ and ${\text{H}}_2\text{O}$

Stopping powers of antiprotons in ${\text{H}}_2$ and ${\text{H}}_2\text{O}$ targets are calculated using a semiclassical time-dependent convergent close-coupling method. In our approach the ${\text{H}}_2$ target is treated using a two-center molecular multiconfiguration approximation, which fully accounts for the electron-electron correlation. Double-ionization and dissociative ionization channels are taken into account using an independent-event model. The vibrational excitation and nuclear scattering contributions are also included. The ${\text{H}}_2\text{O}$ target is treated using a neonization method proposed by C. C. Montanari and J. E. Miraglia [J. Phys. B 47, 015201 (2014)], whereby the ten-electron water molecule is described as a dressed Ne-like atom in a pseudospherical potential. Despite being the most comprehensive approach to date, the results obtained for ${\text{H}}_2$ only qualitatively agree with the available experimental measurements.

Figure 1

Radial distribution functions $|{\chi }_{i,\nu }{\left(d\right)|}^2{d}^2$ of the ${\text{H}}_2$ molecular vibrations with $\nu =0$, 1, and 2 (in a.u.). The potential energy curve and the vibrational energy levels of ${\text{H}}_2$ are shown in units of eV. Note that the potential energy curve is shifted up by 31.7007 eV, which is the ground-state energy of ${\text{H}}_2$ at the equilibrium internuclear separation of 1.4487 a.u.

Figure 2

Total stopping cross section for antiproton incident on molecular hydrogen. Included are the experimental data of Agnello et al. [8], with the shaded region representing the experimental uncertainty. The CCC results are shown by the solid line. The electronic stopping cross sections of Lühr and Saenz [13] and Schiwietz et al. [14, 15] are also shown, along with the results from the Bethe formula. Results previously presented per atom have been multiplied by 2.

Figure 3

Individual contributions to the antiproton-${\text{H}}_2$ total stopping cross section. The solid curve labeled $S_e$:${\text{H}}_2$ is the stopping cross section for the primary electron analytically averaged over all possible molecular orientations with $l_{\max }=5$. The dots are the same, but with $l_{\max }=4$. Similarly, $S_e$:${\text{H}}_2$ (3 or.av.) is for an average over just three perpendicular orientations. $S_e$:DbI and $S_e$:DiI are the stopping cross sections associated with double ionization and dissociative ionization (obtained using the analytic orientation-averaging technique). $S_{\mathrm{n}}$ is the nuclear stopping cross section, and $S_{\mathrm{vib}}$ is the vibrational-excitation contribution.

Figure 4

Electronic stopping cross section for one-electron excitations from the three main orientations of the ${\text{H}}_2$ molecule for antiprotons.

Figure 5

Comparison of the electronic stopping cross sections obtained using the full molecular approach and various H-like approximations.

Figure 6

Electronic stopping cross sections for the antiproton in ${\text{H}}_2\text{O}$.