(Shorten version of the PRC abstract) Alpha-induced reactions on 127I have been studied using the activation technique in order to provide cross section data for the modeling of the astrophysical gamma process. The relative intensity of the 536.1 keV gamma transition was measured precisely, its uncertainty was reduced from 13% to 4%. By measuring the yield of the characteristic X-rays, the cross sections of the 127I(alpha,gamma)131Cs reaction have been determined for the first time close to the astrophysically relevant energy region, at energies 9.50 < Ec.m. < 15.15$ MeV. The 127I(alpha,n)130Cs reaction was studied in the range 9.62 < Ec.m. < 15.15 MeV by measuring the yield of the 536.1 keV gamma-ray and at the lower part of this energy range by counting the characteristic X-rays. A comparison of the resulting cross sections to predictions of statistical model calculations confirmed the predictions of the astrophysically relevant averaged alpha width. Nevertheless, the newly derived stellar reaction rates at gamma process temperatures for 127I(alpha,gamma)131$Cs and its reverse reaction are factors 4-10 faster than previous calculations, due to improvements in the reaction model.
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