Abstract: In the process of measuring the cross section of the (n,γ) reactions of ²³⁸U and ²³²Th by the activation method, the activity of the primary β decay products produced by the reaction products is often used for indirect measurement, thereby the cross section can be obtained. The original formula was modified and the detailed derivation was given in this paper. At the same time, this method was analyzed and discussed based on the revised formula to illustrate the feasibility of this method and the problems in the process of the use.