Neutrino mass limits from a precise determination of ββ-decay rates of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mmultiscripts><mml:mrow><mml:mi mathvariant="normal">Te</mml:mi></mml:mrow><mml:mprescripts/><mml:mrow/><mml:mrow><mml:mn>128</mml:mn></mml:mrow><mml:mrow/><mml:mrow/></mml:mmultiscripts></mml:mrow></mml:math>and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mmultiscripts><mml:mrow><mml:mi mathvariant="normal">Te</mml:mi></mml:mrow><mml:mprescripts/><mml:mrow/><mml:mrow><mml:mn>130</mml:mn></mml:mrow><mml:mrow/><mml:mrow/></mml:mmultiscripts></mml:mrow></mml:math>

Double beta decay of $^{128}\mathrm{Te}$ has been confirmed and the ratio of half-lives for \ensuremath{\beta}\ensuremath{\beta} decay of $^{130}\mathrm{Te}$ and $^{128}\mathrm{Te}$ has been determiend as $^{130}\mathrm{Te}_{1/2}$${/}^{128}$${\mathrm{Te}}_{1/2}$=(3.52\ifmmode\pm\else\textpm\fi{}0.11)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}4}$ by ion-counting mass spectrometry of Xe in ancient Te ores. The Xe measurements, combined with common Pb dating, yield a $^{130}\mathrm{Te}$ half-life of (2.7\ifmmode\pm\else\textpm\fi{}0.1)\ifmmode\times\else\texttimes\fi{}${10}^{21}$ yr and thus a $^{128}\mathrm{Te}$ half-life of (7.7\ifmmode\pm\else\textpm\fi{}0.4)\ifmmode\times\else\texttimes\fi{}${10}^{24}$ yr. These results give limits on the effective Majorana mass of the neutrino (1.1-1.5 eV) and right-handed currents (\ensuremath{\Vert}〈\ensuremath{\eta}〉\ensuremath{\Vert}&gt;5.3\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}8)}$ comparable to the best obtained from direct neutrinoless \ensuremath{\beta}\ensuremath{\beta}-decay searches. They also imply new limits on nonstandard Majorons not constrained by measurements of the ${\mathit{Z}}^{0}$ decay width.