Barkas Effect for Antiproton Stopping in ${\mathrm{H}}_2$

We report the stopping power of molecular hydrogen for antiprotons of kinetic energy above the maximum ($\approx 100\mathrm{k}\mathrm{e}\mathrm{V}$) with the purpose of comparing with the proton one. Our result is consistent with a positive difference in antiproton-proton stopping powers above $\approx 250\mathrm{k}\mathrm{e}\mathrm{V}$ and with a maximum difference between the stopping powers of $21\%\pm 3\%$ at around 600 keV.

Figure 1

Equivalent $\overline{p}$ path length versus equivalent mean annihilation time with the best fit curve described in the text, for various pressures with $E_{\mathrm{c}\mathrm{a}\mathrm{p}}=40\mathrm{e}\mathrm{V}$. For each pressure the arrow indicates the position of the last annihilation vertex in the target. For 150 mbar pressure the arrows indicate the interval between the first and last experimental annihilation vertices.

Figure 2

(a) $\overline{p}$ best stopping power function in ${\mathrm{H}}_2$ (curve 1) with the other analyzed $\overline{p}$ stopping power functions (curves 2–4); the proton behavior superimposed (dotted). (b) Enlargement of (a) in the region above the maximum. Curves 1, 1*, and 4: see text.

Figure 3

$\overline{p}$ path length versus mean annihilation time with best fit curves at different ${\mathrm{H}}_2$ pressures and $E_{\mathrm{c}\mathrm{a}\mathrm{p}}=40\mathrm{e}\mathrm{V}$. From top to bottom: (a) curve 1, (b) curve 2, (c) curve 3, (d) curve 4. The arrows indicate the $E_i$ initial kinetic energy values for the $\overline{p}$ stopping in the gas near the entrance, in the middle, and near the exit wall of the target.

Figure 4

Left column: mean $\overline{p}$ annihilation time versus path length at 150 mbar with the best fit curve 1 $+$ proton (a), $1+4$ (c), 1 (e), $1+1^{*}$ (g); see text. Right column: annihilation time differences (ns) for experimental and best fit curves at different $z$ in the target for the four curves in the left column.