Method for Testing Time-Reversal Invariance in Beta Decay

One of the possible tests of time-reversal invariance in weak interactions is the electron-neutrino angular correlation, for which no polarized nuclei and no measurements of the polarization of emitted electrons are required. If the electron-neutrino angular correlation function, e.g., $1+\left(\frac{p}{3W}\right)f\left(g\right)\mathrm{}cos\theta$ (for $\Delta J=\pm 1$ transitions) has $p$ and/or $Z$ dependences in the measurements of $f\left(g\right)\mathrm{}$ [see Eq. (7)], invariance under time reversal $T$ is not conserved. Conversely, if invariance under $T$ holds, there are no $p$ and $Z$ dependences of $f\left(g\right)\mathrm{}$. In experiments, it is advisable to compare the $f\left(g\right)\text{'}\mathrm{s}$ for electron and positron decays. Furthermore, the experiment will be another possible test of charge-conjugation invariance if time-reversal invariance does not hold.