[en] At the injection area of the RCS ring in the J-PARC, residual gamma dose at the rectangular ceramic ducts, especially immediately downstream of the charge-exchanged foil, has increased with the output beam power. In order to investigate the cause of high residual activities, residual gamma dose and radioactive sources produced at the exterior surface of the ducts have been measured by a GM survey meter and a handy type of Germanium (Ge) semiconductor detector in the case of 181 MeV injected proton beam energy. With these measurements, it is revealed that the radioactive sources produced by nuclear reactions cause the high activities at the injection area. For a better understanding of phenomena in the injection area, various simulations have been done with the PHITS Monte Carlo code. The distribution of radioactive sources and residual gamma dose rate obtained by the calculations are consistent with the measurement results. With this consistency, secondary neutrons and protons derived from nuclear reactions at the charge-exchanged foil are the dominant cause to high residual gamma dose at the ceramic ducts in the injection area. These measurements and calculations are unique approaches to reveal the cause of high residual dose around the foil. This study is essential for the future of high-intensity proton accelerators using a stripping foil. (author)