From coincidence measurements on $\ensuremath{\gamma}\ensuremath{-}\ensuremath{\gamma}$ cascades following the decay of $^{129}\mathrm{Te}^{m}$ the existence of a 1047-keV level in $^{129}\mathrm{I}$ is well established. Angular correlation measurements for several cascades give the following values: ${281\ensuremath{-}251\ensuremath{-}\mathrm{k}\mathrm{e}\mathrm{V}\phantom{\rule{0ex}{0ex}}\mathrm{c}\mathrm{a}\mathrm{s}\mathrm{c}\mathrm{a}\mathrm{d}\mathrm{e}:,{A}_{22}= 0.238\ifmmode\pm\else\textpm\fi{}0.015,,{A}_{44}= 0.014\ifmmode\pm\else\textpm\fi{}0.026;}{209\ensuremath{-}251\ensuremath{-}\mathrm{k}\mathrm{e}\mathrm{V}\phantom{\rule{0ex}{0ex}}\mathrm{c}\mathrm{a}\mathrm{s}\mathrm{c}\mathrm{a}\mathrm{d}\mathrm{e}:,{A}_{22}= 0.234\ifmmode\pm\else\textpm\fi{}0.012,,{A}_{44}= 0.011\ifmmode\pm\else\textpm\fi{}0.022;}{281\ensuremath{-}278\ensuremath{-}\mathrm{k}\mathrm{e}\mathrm{V}\phantom{\rule{0ex}{0ex}}\mathrm{c}\mathrm{a}\mathrm{s}\mathrm{c}\mathrm{a}\mathrm{d}\mathrm{e}:,{A}_{22}=\ensuremath{-}0.048\ifmmode\pm\else\textpm\fi{}0.014,,{A}_{44}=\ensuremath{-}0.014\ifmmode\pm\else\textpm\fi{}0.023;}{209\ensuremath{-}278\ensuremath{-}\mathrm{k}\mathrm{e}\mathrm{V}\phantom{\rule{0ex}{0ex}}\mathrm{c}\mathrm{a}\mathrm{s}\mathrm{c}\mathrm{a}\mathrm{d}\mathrm{e}:,{A}_{22}=\ensuremath{-}0.059\ifmmode\pm\else\textpm\fi{}0.011,,{A}_{44}= 0.018\ifmmode\pm\else\textpm\fi{}0.018;}{624\ensuremath{-}209\ensuremath{-}\mathrm{k}\mathrm{e}\mathrm{V}\phantom{\rule{0ex}{0ex}}\mathrm{c}\mathrm{a}\mathrm{s}\mathrm{c}\mathrm{a}\mathrm{d}\mathrm{e}:,{A}_{22}=\ensuremath{-}0.270\ifmmode\pm\else\textpm\fi{}0.065,,{A}_{44}= 0.047\ifmmode\pm\else\textpm\fi{}0.095;}{624\ensuremath{-}460\ensuremath{-}\mathrm{k}\mathrm{e}\mathrm{V}\phantom{\rule{0ex}{0ex}}\mathrm{c}\mathrm{a}\mathrm{s}\mathrm{c}\mathrm{a}\mathrm{d}\mathrm{e}:,{A}_{22}= 0.151\ifmmode\pm\else\textpm\fi{}0.009,,{A}_{44}= 0.003\ifmmode\pm\else\textpm\fi{}0.012;}{624\ensuremath{-}478\ensuremath{-}\mathrm{k}\mathrm{e}\mathrm{V}\phantom{\rule{0ex}{0ex}}\mathrm{c}\mathrm{a}\mathrm{s}\mathrm{c}\mathrm{a}\mathrm{d}\mathrm{e}:,{A}_{22}=\ensuremath{-}0.290\ifmmode\pm\else\textpm\fi{}0.025,,{A}_{44}=\ensuremath{-}0.002\ifmmode\pm\else\textpm\fi{}0.036;}{343\ensuremath{-}460\ensuremath{-}\mathrm{k}\mathrm{e}\mathrm{V}\phantom{\rule{0ex}{0ex}}\mathrm{c}\mathrm{a}\mathrm{s}\mathrm{c}\mathrm{a}\mathrm{d}\mathrm{e}:,{A}_{22}=\ensuremath{-}0.341\ifmmode\pm\else\textpm\fi{}0.058,,{A}_{44}= 0.033\ifmmode\pm\else\textpm\fi{}0.080.}$ These values, together with nuclear orientation data, uniquely determine the spin of the excited states at 278 keV ($\frac{3}{2}$) and 860 keV ($\frac{3}{2}$). The mixing ratios $\ensuremath{\delta}(\frac{E2}{M1})$ for the different transitions are obtained.[RADIOACTIVITY $^{129}\mathrm{Te}$ from $^{128}\mathrm{Te}(n,\ensuremath{\gamma})$; measured $\ensuremath{\gamma}\ensuremath{\gamma}$ coin, $\ensuremath{\gamma}\ensuremath{\gamma}(\ensuremath{\theta})$. $^{129}\mathrm{I}$ deduced levels, $J$, $\ensuremath{\gamma}$-mixing ratios. Enriched target, Ge(Li), Na(Tl) detectors.]
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