because of nearly identical total-inelastic and annihilation cross-sections. When examining the ratio of the resulting [$^3\overline{\text{He}}~$]{}to [$\overline{\text{D}}~$]{}flux, we see in Fig. \[fig:propagation\], an enhancement (suppression) of order $25\%$ when using the annihilation (total-inelastic) cross-sections.

Now that the dark matter properties and propagation models have been fixed and the transport equation solved, we can translate the injection spectra calculated in Sec. \[sec:production\] into detectable fluxes at the top of the Earth’s atmosphere.

[$^3\overline{\text{He}}~$]{}Flux and Detection Prospects for Current and Future Experiments {#sec:experiments}
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We have calculated injection spectra and propagation functions for [$^3\overline{\text{He}}~$]{}, discussed the most important differences with respect to [$\overline{\text{D}}~$]{}, and presented ratios for the conversion of [$\overline{\text{D}}~$]{}spectrum into [$^3\overline{\text{He}}~$]{}. For concreteness, we reiterate the procedure here and show the most important scaling relations.

With an antideuteron flux (or event rate) $\Phi_{\overline{D}}$ calculated within the coalescence framework described in Sec. \[sec:production\], the antihelium flux is related through the following equation: $$\begin{split}
\Phi_{\overline{He}} (T_{\mathrm{TOA}}) = R_{\textrm{IS}}(T_{\mathrm{IS}}) \cdot R_{\textrm{solar}}(T_{\mathrm{IS}})\left(\frac{p_0^{A=3}}{\overline{p}_{A=3} }\right)^6 \times \\
\times \left(\frac{{\overline{p}_{A=2}}}{p_0^{A=2}} \right)^3 \cdot R_{\text{PP}}(T_{\mathrm{IS}},m_\chi,f) \cdot \Phi_{\overline{D}} (T_{\mathrm{IS}}-e\phi_F/2),
\end{split}$$

where $\overline{p}_{A=3}$ = 0.357 GeV/c and $\overline{p}_{A=2}$ = 0.192 GeV/c. Here, $T_{\mathrm{IS}}=T_{\mathrm{TOA}}+(2/3)~e\phi_F$. $R_{\mathrm{PP}}$ is the particle production ratio, shown for GAPS energies from Fig. \[fig:ratios\] for the benchmark coalescence momenta. 