Test of the Nature of the Vector Interaction inβDecay
An experiment is proposed to test the theory recently advanced by Feynman and Gell-Mann on the vector interaction in $\ensuremath{\beta}$ decay. According to the theory, the Fermi coupling constant is not appreciably altered by renormalization, in agreement with experiment. A further property of the theory is exploited here, that analogous $\ensuremath{\gamma}$ and $\ensuremath{\beta}$ transitions in light nuclei have proportional matrix elements, as far as the $V$ interaction is concerned. In particular, the $V$ interaction gives rise to "weak magnetism" analogous to the magnetic effects that induce the emission of $M1$ photons. This "weak magnetism" obeys Gamow-Teller selection rules and interferes with the $A$ coupling, distorting the spectra of high-energy $\ensuremath{\beta}$ transitions with $\ensuremath{\Delta}J=1$ (no).It is suggested that the $\ensuremath{\beta}$ spectra of ${\mathrm{B}}^{12}$ and ${\mathrm{N}}^{12}$ be measured accurately and compared. Departure from linearity of the Kurie plot should be noticed in each case; the ratio of the spectra can be calculated with confidence on the basis of the theory, which predicts a 20% effect. The measured $\ensuremath{\gamma}$-ray width of the 15.11-Mev state in ${\mathrm{C}}^{12}$ is used in the calculation.