Prospects for Far Infrared Observations of Hydrogen Recombination Lines in Epoch of Reionization Galaxies

The possibility of detecting distant galaxies at redshifts $z = 6{-} 10$ in hydrogen recombination lines is considered. We showed that, for a 10-m cooled space telescope with a multipixel grating spectrometer, detection of sources is possible over a time of about 1000 hours when observing regions enhanced with gravitational lensing by galaxy clusters. We present the dependence of the expected number of detected sources on the observation time for a number of lens clusters. Criteria have been developed for choosing between the deepest survey of one region, or the division of observation time between several regions.