A numerical method of analyzing beta decay measurements and its application to the 1− → 0+ transitions of170Tm,186Re and210Bi

A numerical method is proposed for determining nuclear matrix elements from beta decay measurements. The method is based on the least squares principle, and its main application is the analysis of beta ray spectra. Its main result is to show that a spectrum shape measurement usually determines only a second order polynomial of the matrix elements to a high precision whereas each of the matrix elements can vary within wide limits. The method is applied to the first forbidden non unique transitions (1^?→ 0⁺) of¹⁷⁰Tm,¹⁸⁶Re and²¹⁰Bi (RaE). The 3 contributing matrix elements and their ranges of error are determined from recent measurements.