Apparent absence of electromagnetic or strong-interaction time-reversal violation in the decay ofHfm180

Time reversal $T$ invariance in the nuclear interaction was investigated by observing the directional correlation of the strongly hindered 501-keV $\gamma$ ray of ${}_{}{}^{180}{}_{}{}^{}\mathrm{Hf}$ with the subsequent 332- and 215-keV $\gamma$ rays from a source of ${}_{}{}^{180}{}_{}{}^{}\mathrm{Hf}_{}^{\mathrm{m}}{}_{}{}^{}$ polarized at low temperatures. The asymmetry of the correlation was measured to be (2.8±5.1)× ${10}^{-4\mathrm{}}$, corresponding to a phase angle between the 501-keV $E3\mathrm{}$ and $M2\mathrm{}$ multipoles given by $sin\eta =0.048\mathrm{}\pm 0.087$, consistent with the assumption of $T$ invariance. Upper limits on the out-of-phase components of the $E3\mathrm{}$ and $M2\mathrm{}$ matrix elements were determined to be 3× ${10}^{-6\mathrm{}}$ and 1× ${10}^{-8\mathrm{}}$ Weisskopf units, respectively; these extremely small upper limits result from the use of a strongly hindered $\gamma$ ray. In addition, based on these results, estimates of the magnitude of the $T$-odd potential were deduced, from which we conclude that the millistrong or electromagnetic interactions are unlikely to be a source of $T$ violations.