largely cancel after applying [$\bar{p}~$]{}constraints from PAMELA while the uncertainty in the $A=3$ coalescence momentum leads to a flux uncertainty of 1-3 orders of magnitude (not-shown), independent of [$\bar{p}~$]{}constraints. The astrophysical [$^3\overline{\text{He}}~$]{}background peaks with a flux of $10^{-12}$ \[m$^2$ s sr GeV/n\]$^{-1}$ at approximately 20 GeV/n [@duperray2005]. This is off-scale over all energies shown and rapidly declines at lower energies. By 1 GeV/n the flux has already dropped by another factor $10^2$. Over the low energies covered by GAPS it can be considered zero relative to the primaries.

For the case of decaying dark matter, the flux can be easily estimated from the annihilation case by modifying terms in Eq. (\[eq:pnum\]). First, the squared terms become linear as the reaction rate now traces the dark matter density $\rho_{\rm DM}$ rather than $\rho_{\rm DM}^2$. The numerical factor and thermal cross-section can then be replaced by finding an ‘equivalent lifetime’, $\tau$, which provides an average flux equal to the annihilation case (for $\langle \sigma v \rangle=3 \times 10^{-26} {\rm cm}^3/{\rm s}$). The term containing $\langle \sigma v \rangle$ is then replaced by $(\tau_0/\tau)$. As benchmarks, for dark matter decaying to $b\bar{b}$ with mass $m_{\chi}^{\rm dec}=20$ GeV we find $\tau_0 \approx 7.5 \times 