Integral method for fitting nuclear decay chains

The conventional method for determining unknown half-lives of isotopes in data that have many decay chains is by fitting radioactive decay curves using the Bateman equations. The fit gets difficult in cases with very low statistics on the fast-decaying components. To compensate for the low statistics, we propose a new method for fitting and extracting these half-lives. The new method consists of making a cumulative sum histogram of all the counts recorded from the radioactive isotope, then fitting the histogram with an integral of the Bateman method. An extensive analysis of this method was conducted with varying statistics, length of the decay chain, and a range of half-lives within the decay chains using simulated data. In this work we show results from the analysis and the new algorithm which was used to test the integral method. The utility of the integral method will also be discussed based on the results of the algorithm.