A thorough search of the sky exposed at the Pierre Auger Cosmic Ray Observatory reveals no statistically significant excess of events in any small solid angle that would be indicative of a flux of neutral particles from a discrete source. The search covers from -90 to +15 degrees in declination using four different energy ranges above 1 EeV (10^18 eV). The method used in this search is more sensitive to neutrons than to photons. The upper limit on a neutron flux is derived for a dense grid of directions for each of the four energy ranges. These results constrain scenarios for the production of ultra-high energy cosmic rays in the Galaxy.
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