Positronium formation from positron impact on hydrogen and helium targets

Charge-exchange cross sections are presented for collisions of positrons with hydrogen and neutral and singly ionized helium targets using a variant of the classical trajectory Monte Carlo approach. As a check on the method a comparison is made with the corresponding proton results. An extended error analysis is presented. Reasonable agreement with available experimental data is found, and the charge-exchange cross section for positrons on ${\text{He}}^{+}$ is predicted.

Figure 1

Statistical error as a function of $n_q$, with $n=10000$.

Figure 2

Charge-exchange cross sections for proton collisions with neutral hydrogen: our theoretical calculations, CTMCc with (3) enforced (crosses), and CTMC without threshold correction and where (3) was not enforced (solid diamonds) compared with the absolute experimental data of [20] (solid circles).

Figure 3

Charge-exchange cross sections for positron collisions with neutral hydrogen: CTMCc (crosses) and CTMC (solid diamonds) compared with the absolute experimental data of [24] (solid circles).

Figure 4

Plot of $p^2|F_{10}\left(p{|}^2\right)$ for hydrogenic ions against the magnitude of the momentum $p$ for various values of $\overline{Z}$ as well as the equivalent Byron-Joachain momentum distribution for helium: $\overline{Z}=1.344$, solid line; $\overline{Z}=1.47$, dotted line; $\overline{Z}=1.6875$, dash-dotted line; Byron-Joachain, dashed line.

Figure 5

Charge-exchange cross sections for proton collisions with neutral helium: CTMC (crosses) compared with the absolute experimental data of [35] (solid circles).

Figure 6

Positronium-formation cross sections for positron collisions with neutral helium: threshold-corrected CTMC ($\overline{Z}=1.47$; crosses) compared with the absolute experimental data of [11, 36] (solid circles).

Figure 7

Charge-exchange cross sections for proton collisions with He${}^{+}$: CTMC (crosses) compared with the absolute experimental data of [41] (solid circles) and [42] (open circles).

Figure 8

Positronium-formation cross sections for positron collisions with He${}^{+}$ in the threshold-corrected CTMC (crosses).

Figure 9

Positronium-formation cross sections for positron collisions with neutral and singly ionized helium: solid blue curve, high-order polynomial fit to the absolute experimental data of [11, 36] for neutral helium; dashed red curve, high-order polynomial fit to our CTMC calculations for He${}^{+}$.