The narrow positron annihilation line source in the Galactic center ha
s been identified with the X-ray source 1E 1740.7-2942, which is coinc
ident in projection with a Galactic center molecular cloud and exhibit
s synchrotron jets in the radio spectrum. It has been suggested that t
he source is powered by Bondi-Hoyle accretion from the cloud onto a co
mpact object. Here we show that, regardless of the source of the X-ray
luminosity, the irradiation of the interstellar medium (ISM) in its v
icinity by similar to 1 keV X-rays can generate substantial luminositi
es in a number of far-infrared atomic fine-structure lines, such as [O
I] 63 mu m, [C II] 158 mu m, and [Si II] 35 mu m. Similar predictions
hold for the nearly identical (in luminosity, spectrum, and presence
of radio jets) Galactic center source GRS 1758-258. The corresponding
line fluxes will be easily detectable using the Infrared Space Observa
tory; if the sources are embedded in dense ISM, the observations will
allow estimates of the gas density, column density, and volume filling
factor in the vicinity of the X-ray sources, the X-ray luminosity of
the source averaged over the last t similar to 100 yr, and will constr
ain models for accretion from the ISM.