Moskalenko, Strong, & Ormes [@moskalenko2001] for the total inelastic, non-annihilating inelastic, and annihilation cross sections. For an atomic nucleus ($A,|Z|$) impingent on a stationary proton with kinetic energy per nucleon $T$, these are given in mb by $$\begin{gathered}
\begin{split}
\sigma^{\mathrm{tot}}_{\bar{p}A} = A^{2/3} [48.2+19 T^{-0.55} &+ (0.1-0.18T^{-1.2})Z \\
&+0.0012 T^{-1.5}Z^2]
\end{split}\\
\sigma^{\mathrm{ann}}_{\bar{p}A} = \sigma^{\mathrm{tot}}_{\bar{p}A}-\sigma^{\mathrm{non-ann}}_{\bar{p}A}\\ 
\sigma^{\mathrm{non-ann}}_{\bar{p}A} = \sigma^{\mathrm{inel}}_{pA}\end{gathered}$$ In the last equation, we assume that the non-annihilating inelastic cross-section for an antiproton-nucleus interaction is the same as the proton-nucleus interaction which can be well-approximated by $$\begin{aligned}
\begin{split}
\sigma_{pA}^{\mathrm{inel}} &=45 A^{0.7} \left[1+0.016 \sin(5.3-2.63\ln A)\right] \\
&\times  \left\{
\begin{array}{ll}
1-0.62 e^{-T/0.2} \sin\left[\frac{10.9}{(10^3T)^{0.28}}\right], & T \leq 3;\\
1,                                                                  & T > 3;
\end{array} \right.\nonumber\\
\end{split}\end{aligned}$$

In Figure \[fig:cross-sections\] we plot the three cross-sections for antihelium and antideuterons as a function of the kinetic energy per nucleon. For the special case of [$\overline{\text{D}}~$]{}, we take the parameterization from Tan & Ng [@tan1983] for total-inelastic cross-section, and an empirically determined non-annihilating inelastic cross-section which is very small due to the exceptionally low binding energy of [$\overline{\text{D}}~$]{}[@duperray2005]. Peaking at approximately 4 mb, this leads to a much higher probability of annihilation during inelastic scattering than the antihelium case. We see that antihelium posesses an inelastic cross-section roughly 2 