Improved measurement of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mn>2</mml:mn><mml:mi>ν</mml:mi><mml:mi>β</mml:mi><mml:mi>β</mml:mi></mml:mrow></mml:math>half-life of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mrow/><mml:mn>136</mml:mn></mml:msup></mml:math>Xe with the EXO-200 detector

We report on an improved measurement of the $2\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ half-life of ${}^{136}$Xe performed by EXO-200. The use of a large and homogeneous time-projection chamber allows for the precise estimate of the fiducial mass used for the measurement, resulting in a small systematic uncertainty. We also discuss in detail the data-analysis methods used for double-$\ensuremath{\beta}$ decay searches with EXO-200, while emphasizing those directly related to the present measurement. The ${}^{136}$Xe $2\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ half-life is found to be ${T}_{1/2}^{2\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}}$ = $2.165\ifmmode\pm\else\textpm\fi{}0.016(\mathrm{stat})\ifmmode\pm\else\textpm\fi{}0.059(\mathrm{sys})\ifmmode\times\else\texttimes\fi{}{10}^{21}$ yr. This is the most precisely measured half-life of any $2\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ decay to date.