Measurement of the double-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>β</mml:mi></mml:mrow></mml:math>decay half-life of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mmultiscripts><mml:mi mathvariant="normal">Nd</mml:mi><mml:mprescripts/><mml:none/><mml:mrow><mml:mn>150</mml:mn></mml:mrow></mml:mmultiscripts></mml:math>and search for neutrinoless decay modes with the NEMO-3 detector

The half-life for double-$\ensuremath{\beta}$ decay of $^{150}\mathrm{Nd}$ has been measured by the NEMO-3 experiment at the Modane Underground Laboratory. Using 924.7 days of data recorded with $36.55$ g of $^{150}\mathrm{Nd}$, we measured the half-life for $2\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ decay to be ${T}_{1/2}^{2\ensuremath{\nu}}=(9.{11}_{\ensuremath{-}0.22}^{+0.25}(\mathrm{stat}.)\ifmmode\pm\else\textpm\fi{}0.63(\mathrm{syst}.))\ifmmode\times\else\texttimes\fi{}{10}^{18}$ yr. The observed limit on the half-life for neutrinoless double-$\ensuremath{\beta}$ decay is found to be ${T}_{1/2}^{0\ensuremath{\nu}}&gt;1.8\ifmmode\times\else\texttimes\fi{}{10}^{22}$ yr at $90%$ confidence level. This translates into a limit on the effective Majorana neutrino mass of $\ensuremath{\langle}{m}_{\ensuremath{\nu}}\ensuremath{\rangle}&lt;4.0\text{\ensuremath{-}}6.3$ eV if the nuclear deformation is taken into account. We also set limits on models involving Majoron emission, right-handed currents, and transitions to excited states.