Calibrations of Beta and Gamma Detector Efficiencies

The $^{12}$C+$^{13}$C reaction has been studied at sub-barrier energies from Ec.m.=2.55 MeV to 4.7 MeV by detecting the decay of $^{24}$Na resulting from the proton decay branch of the compound nucleus $^{25}$Mg. To determine the absolute cross section, two different methods, coincidence method and sum peak method, have been applied to determine the detector efficiency and the total amount of the produced $^{24}$Na. A calibrated $^{22}$Na standard source has been used to validate the sum-peak method. The angular correlation effect of the two coincident gamma rays from the $^{24}$Na decay was corrected by means of the Monte Carlo simulations. Applying the sum-peak method to the $^{22}$Na experimental data, the reference value for the activity and the activity obtained experimentally agreed within a range of 1\%.