Measurement of the Relativistic Doppler Effect Using 8.6-MeV CaptureγRays

The energies of $\gamma$ rays from the 10.27-MeV $(T=1, \Gamma <1.8\mathrm{} \mathrm{keV})\to 1.63-\mathrm{MeV}$ ($T=0\mathrm{}$) transition in ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$ have been measured in an annular Ge (Li) detector at 0 and 180°. ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}({}_{}{}^4{}_{}{}^{}\mathrm{He}, \gamma )$ and ${}_{}{}^4{}_{}{}^{}\mathrm{He}({}_{}{}^{16}{}_{}{}^{}\mathrm{O}, \gamma )$ capture reactions in a differentially pumped gas target were used to produce recoiling ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$ ions with two different very accurately known velocities. We observe a tranverse Doppler shift of 10.09 ± 0.41 keV for the ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ capture reaction. This allows us to determine relativistic time-dilation effects at velocities of $0.05c$ to an accuracy of 3.5%. Our results are in very good agreement with the prediction of special relativity.