Test of Time-Reversal Invariance and Measurements of Positron and Neutrino Asymmetries in PolarizedNe19Beta Decay

We present a comprehensive discussion of an experiment, previously reported, to test time-reversal ($T$) invariance in the $\beta$ decay of ${}_{}{}^{19}{}_{}{}^{}\mathrm{Ne}$. The "time-reversal" coefficient $D$, as well as the neutrino and positron asymmetry coefficients $B$ and $A$, respectively, is measured, with results as follows: $D=+0.002\mathrm{}\pm 0.014$, $B=-0.90\mathrm{}\pm 0.13$, and $A=-0.039\mathrm{}\pm 0.002$. The value of $D$, based on 30 000 events, is consistent with $T$ invariance: $T$ invariance implies $D=0\mathrm{}$, since final-state corrections to $D$ are negligible. The atomic-beam method is used to form a nuclear-spin polarized beam of ${}_{}{}^{19}{}_{}{}^{}\mathrm{Ne}$ atoms in the ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ ground state. Coefficients $D$ and $B$ are measured by observing correlations between the positron and recoil ion ${}_{}{}^{19}{}_{}{}^{}\mathrm{F}_{}^{-}{}_{}{}^{}$ (in delayed coincidence) with respect to the ${}_{}{}^{19}{}_{}{}^{}\mathrm{Ne}$ spin polarization, from decays in flight. The beam terminates its flight in a cell where ${}_{}{}^{19}{}_{}{}^{}\mathrm{Ne}$ atoms are captured and remain for approximately 3 sec but suffer no significant depolarization. Positrons emitted parallel and antiparallel to the spin by ${}_{}{}^{19}{}_{}{}^{}\mathrm{Ne}$ decaying in the cell are counted to measure $\beta$. The results of our measurements are compared with similar observations of the $A$ decay of polarized neutrons.