Beta-ray spectra of 12B and 12N and conserved vector current

In order to investigate spectral shape factors of ¹²B and ¹²N, we make a new formalism of β-decay theory, where the radial wave functions of leptons are treated with no approximation and, therefore, the nuclear matrix elements are electron-energy dependent. With this formalism we can show strong support for the conserved vector current hypothesis in analyzing the experimental data which were given by Wu, Lee and Mo in 1963 and revised by them in 1977 using the latest experimental results on the end-point energies and branching ratios of the inner β-groups, in addition to the correct Fermi functions for the positron. In fact, the average slopes of the spectral shape factors for ¹²B and ¹²N are in excellent agreement with those in our theory. Recent experimental data given by the Heidelberg group are also in good agreement with the theory if we analyze the difference of the average slopes for ¹²B and ¹²N. There are, however, small discrepancies with the theory in their individual values. The relation of the present formalism with traditional theories of β-decay is discussed.