Nuclear Spin-Electron-Neutrino Correlation in ForbiddenβDecay

The distribution function correlating the electron and neutrino momenta with the spin orientation of the parent or daughter nucleus is calculated for forbidden transitions with Coulomb effects included. Attention is focused on the $\beta$-decay interaction law form and behavior under time reversal. The near equivalence of the $\mathrm{VA}$ and $\mathrm{STP}$ forms is noted and a generalized substitution law relating the $\mathrm{VA}$, $\mathrm{STP}$, and $\mathrm{VASTP}$ forms is derived. A number of experiments distinguishing between the $\mathrm{VA}$ and $\mathrm{STP}$ forms are discussed in detail. Lastly, experiments testing time-reversal invariance are discussed with special emphasis placed on those terms in the distribution function which are not due to Fierz-like interferences and are not obscured by Coulomb effects.