Induced Effects inβDecay

Formulas for $\beta$-decay spectra are calculated for Gamow-Teller allowed and first-forbidden unique selection rules. Included are all possible effects induced by strong interactions, up to first order in momentum transfer. From the measured ratio of ${\mathrm{B}}^{12}$ and ${\mathrm{N}}^{12}$ $\mathrm{ft}$ values, and from the assumption that the reduced nuclear matrix elements for these transitions are identical, a relation is deduced between the magnitudes of the two possible induced couplings in the axial vector interaction (the "induced tensor" and "induced pseudoscalar" couplings). The "induced pseudoscalar" coupling must be small in order to produce the observed rate of $\mu$ capture in ${\mathrm{C}}^{12}$, which suggests that the ${\mathrm{B}}^{12}$-${\mathrm{N}}^{12}$ $\mathrm{ft}$ ratio is due primarily to the "induced tensor" coupling. Positive evidence of an "induced tensor" coupling might be obtained from a careful measurement and analysis of the first-forbidden unique $\beta$ spectrum of ${\mathrm{N}}^{16}$.