The flux-weighted average cross-sections for the 59Co($ \gamma$, xn)58-55Co reactions have been measured with the bremsstrahlung end-point energies of 65 and 75 MeV by using the activation method in combination with the off-line $ \gamma$-ray spectrometry. The measured cross-sections for the $ (\gamma,\mathrm{n})$, $ (\gamma,2\mathrm{n})$, $ (\gamma,3\mathrm{n})$ and $ (\gamma,4\mathrm{n})$ reactions of 59Co at 65 MeV are $ 15.828\pm 0.491$, $ 5.003\pm 0.206$ , $ 0.408\pm 0.047$ and $ 0.039\pm 0.008$ mb, whereas at 75 MeV are $ 15.653\pm 0.361$, 4.965±0.289, $ 0.389\pm 0.062$ and $ 0.036\pm 0.007$ mb, respectively. The 59Co($ \gamma$, xn) reaction cross-sections as a function of photon energy were also theoretically simulated by using TALYS 1.9 code. Then the flux-weighted average cross-sections at different bremsstrahlung energies were obtained from the theoretical values and the literature data at lower energy based on mono-energetic photons. The present data are measured for the first time and are found to be in good agreement with the theoretical flux-weighted average values. It was found that the 59Co($ \gamma$, xn)58-55Co reaction cross-sections increase from their threshold values to a certain bremsstrahlung energy. After a certain energy, the individual 59Co($ \gamma$, xn) reaction cross-sections decrease with the increase of bremsstrahlung energy due to opening of other reaction channels. These two observations indicate the role of excitation energy and its partition in different reaction channels. All the four cobalt isotopes produced from the 59Co($ \gamma$, xn) reactions have medical and other applications.
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