  Context. Since 1996, during periods of low solar activity, the HSTOF
instrument onboard the SOHO satellite has been measuring weak fluxes of He
atoms of 28-58 keV/n (helium energetic neutral atoms - He ENA). The probable
source region is the inner heliosheath.
  Aims. We aim to understand the emission mechanism of He ENA based on
knowledge of heliosheath spatial extent and plasma content resulting from
Voyager 1 & 2 measurements in the period after termination shock crossings.
  Methods. He ENA are generated by charge-exchange neutralization of energetic
helium ions on interstellar neutral H and He. Energy spectra of helium ions in
the heliosheath are calculated by following the evolution of their velocity
distribution functions when carried by and undergoing binary interactions with
plasma constituents of a background flow whose particle populations are modeled
to approximately render post-termination-shock Voyager data.
  Results. The observed HSTOF He ENA form a higher energy part of general
heliospheric He ENA fluxes and can be explained by the proposed mechanism to
within 2{\sigma} error. The main factor determining the level of emission (and
its uncertainty) is the energy spectrum of He^+ pickup ions in post-termination
shock plasmas.
