The activation method is proposed for collection of the sufficient statistics during the investigation of the nuclear astrophysical reactions at low energies with the short-living residual nuclei formation. The main feature is a multiple cyclical irradiation of a target by an ion beam and measurement of the radioactivity decay curve. The method was tested by the yield measurement of the 12 C( p ,γ) 13 N reaction with detecting the annihilation γγ- coincidences from 13 N(β + ν) 13 C decay at the two-arm scintillation spectrometer.