Test of time reversal invariance in ^{57}Fe

An experiment has been performed to test time reversal invariance by observing the angular distribution of the linear polarization of the mixed $E2$ and $M1$ 122 keV $\ensuremath{\gamma}$ rays in $^{57}\mathrm{Fe}$ emitted from oriented $^{57}\mathrm{Co}$ nuclei. Nuclear orientation was achieved with a high magnetic field (the 288 kG hyperfine field of $^{57}\mathrm{Co}$ in an iron lattice) and a low temperature (16.5 to 18 mK obtained with a $^{3}\mathrm{He}$-$^{4}\mathrm{He}$ dilution refrigerator). If time reversal invariance is violated, a term in the angular distribution of the form $(\stackrel{\ensuremath{\rightarrow}}{\mathrm{J}}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}\ifmmode\times\else\texttimes\fi{}\stackrel{\ensuremath{\rightarrow}}{E})(\stackrel{\ensuremath{\rightarrow}}{\mathrm{J}}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}})(\stackrel{\ensuremath{\rightarrow}}{\mathrm{J}}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{\ensuremath{\rightarrow}}{E})sin\ensuremath{\eta}$ would be present, where the vectors $\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}$ and $\stackrel{\ensuremath{\rightarrow}}{E}$ describe the propagation and linear polarization of the $\ensuremath{\gamma}$ ray, respectively, and $\stackrel{\ensuremath{\rightarrow}}{\mathrm{J}}$ is the nuclear orientation vector. The quantity $\ensuremath{\eta}$ is the phase angle between the $E2$ and $M1$ matrix elements of the $\ensuremath{\gamma}$ transition. In our experiment the linear polarization was measured with a Compton polarimeter using an aluminum scatterer and NaI(Tl) detectors. From the observed asymmetry of $A=(\ensuremath{-}0.35\ifmmode\pm\else\textpm\fi{}0.78)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$, a value of $sin\ensuremath{\eta}=(\ensuremath{-}3.1\ifmmode\pm\else\textpm\fi{}6.5)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ was obtained. This result is consistent with time reversal invariance. Possible small contributions to the phase angle from atomic and nuclear final state effects are discussed.