We present new data on the \(^{63}\) Cu( \(\gamma\) , n) cross-section studied using a quasi-monochromatic and energy-tunable \(\gamma\) beam produced at the Shanghai Laser Electron Gamma Source to resolve the long-standing discrepancy between existing measurements and evaluations of this cross-section. Using an unfolding iteration method, \(^{63}\) Cu( \(\gamma\) , n) data were obtained with an uncertainty of less than 4%, and the inconsistencies between the available experimental data were discussed. The \(\gamma\) -ray strength function of \(^{63}\) Cu( \(\gamma\) , n) was successfully extracted as an experimental constraint. We further calculated the cross-section of the radiative neutron capture reaction \(^{62}\) Cu(n, \(\gamma\) ) using the TALYS code. Our calculation method enables the extraction of (n, \(\gamma\) ) cross-sections for unstable nuclides.