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The long-lived radioisotope (36)Cl (half-life: 301,000 years) was measured in granite samples exposed to A-bomb neutrons at distances from 94 to 1,591 m from the hypocenter in Hiroshima, by means of accelerator mass spectrometry (AMS). Measured (36)Cl/Cl ratios decrease from 1.6 x 10(-10) close to the hypocenter to about 1-2 x 10(-13), at a distance of 1,300 m from the hypocenter. At this distance and beyond the measured (36)Cl/Cl ratios do not change significantly and scatter around values of 1-2 x 10(-13). These findings suggest that the (36)Cl had been predominantly produced by thermalized neutrons from the A-bomb via neutron capture on stable (35)Cl, at distances from the hypocenter smaller than about 1,200 m. At larger distances, however, confounding processes induced by cosmic rays or neutrons from the decay of uranium and thorium become important. This hypothesis is theoretically and experimentally supported in a consecutive paper. The results are compared to calculations that are based on the most recent dosimetry system DS02. Close to the hypocenter, measured (36)Cl/Cl ratios are lower than those calculated, while they are significantly higher at large distances from the hypocenter. If the contribution of the cosmic rays and of the neutrons from the decay of uranium and thorium in the sample was subtracted, however, no significant deviation from the DS02 calculations was observed, at those distances. Thus, the Hiroshima neutron discrepancy reported in the literature for (36)Cl for samples from large distances from the hypocenter, i.e., higher measured (36)Cl/Cl ratios than predicted by the previous dosimetry system DS86, was not confirmed.