Collisions of antiprotons with hydrogen molecular ions

Time-dependent close-coupling calculations of the ionization and excitation cross section for antiproton collisions with molecular hydrogen ions are performed in an impact energy range from 0.5 keV to 10 MeV. The Born-Oppenheimer and Franck-Condon approximations as well as the impact parameter method are applied in order to describe the target molecule and the collision process. It is shown that three perpendicular orientations of the molecular axis with respect to the trajectory are sufficient to accurately reproduce the ionization cross section calculated by Sakimoto [Phys. Rev. A 71, 062704 (2005)] reducing the numerical effort drastically. The independent-event model is employed to approximate the cross section for double ionization and ${\text{H}}^{+}$ production in antiproton collisions with ${\text{H}}_2$.

Figure 1

Sketch of the molecule-fixed frame. The $z^{\prime }$ axis is parallel to the internuclear axis of the $\text{H}_2{}^{+}$. Shown are three trajectories of the $\overline{p}$ and the corresponding impact parameters $\mathbf{b}$ for the orientations (i), (ii), and (iii), which are further explained in the text.

Figure 2

(Color online) Cross section for $\overline{p}+\text{H}_2{}^{+}$ as a function of the antiproton impact energy. Black solid curve with plus, present results (orientationally averaged); green circles, calculation by Sakimoto [41]. (a) Ionization, (b) excitation.

Figure 3

(Color online) The transition probability $p\left(b\right)$ and $bp\left(b\right)$—weighted with $b$—for $\overline{p}+\text{H}_2{}^{+}$ collisions as a function of the impact parameter $b$ for different molecular orientations and $E=125\text{keV}$. $p\left(b\right)$: red dotted curve, $\left(\Theta ,\Phi \right)=\left(0,0\right)$; blue solid curve, $\left(\pi /2,0\right)$; green dashed curve, $\left(\pi /2,\pi /2\right)$. $bp\left(b\right)$: red circles, (0,0); blue squares, $\left(\pi /2,0\right)$; green triangles, $\left(\pi /2,\pi /2\right)$. (a) Ionization, (b) excitation.

Figure 4

(Color online) Ionization cross section ${\sigma }_{\text{ion}}$ and excitation cross section ${\sigma }_{\text{exc}}$ for $\overline{p}+\text{H}_2{}^{+}$ as a function of the antiproton impact energy for different molecular orientations. Black pluses, orientationally averaged; red circles, $\left(\Theta ,\Phi \right)=\left(0,0\right)$; blue squares, $\left(\pi /2,0\right)$; green triangles, $\left(\pi /2,\pi /2\right)$. (a) Ionization, (b) excitation.

Figure 5

(Color online) Cross sections leading to the production of ${\text{H}}^{+}$ in collisions with ${\text{H}}_2$ targets as a function of the projectile energy. $\overline{p}$ impact. Present results. $\overline{p}$: red stars, double ionization ${\sigma }_{\text{di}}$; blue triangles, ionization and excitation ${\sigma }_{\text{ie}}$; green plus, summed ${\text{H}}^{+}$ production ${\sigma }_{{\text{H}}^{+}}=2{\sigma }_{\text{di}}+{\sigma }_{\text{ie}}$. $p$: violet X, ${\text{H}}^{+}$ production ${\sigma }_{{\text{H}}^{+}}$. Experimental data: black squares, total ${\text{H}}^{+}$ production for $\overline{p}+{\text{H}}_2$ [1]; black circles, dissociative ionization for $p+{\text{H}}_2$ [36]. The inset shows a high-energy cutout of the same data.