Beta-Gamma Correlation and Time-Reversal Invariance

The distribution function for the first-forbidden beta-gamma correlation for randomly oriented nuclei, including beta transverse polarization terms, is presented and discussed in connection with the question of time-reversal invariance. Coulomb field effects are included and it is found that even for relatively small $Z$ the time-reversal testing asymmetry is reduced appreciably compared to that calculated for $Z=0\mathrm{}$ by Curtis and Lewis. In the limit of high ($\frac{\alpha Z}{2R}$), that is, for most first-forbidden decays, a definite relation exists between the ordinary directional correlation asymmetry and the beta polarization-dependent asymmetries. In this approximation it is found that terms which test time-reversal invariance appear in the same manner in all asymmetries but are dominated in general by contributions which do not test time-reversal invariance. For the particular case of ${\mathrm{Au}}^{198}$ it is shown that the experimental results are consistent with time-reversal invariance but are also consistent with an appreciable violation of time-reversal invariance. It is concluded that under favorable conditions it is barely possible that an investigation of the asymmetries for some other beta-gamma cascade could provide a test for time-reversal invariance. However, the extent to which this invariance is or is not violated could not be determined by such an investigation.