Measurement of the double-β decay of ${}^{150}$Nd to the 0${}_1^{+}$ excited state of ${}^{150}$Sm in NEMO-3

The NEMO-3 results for the double-β decay of ${}^{150}$Nd to the 0${}_1^{+}$ and 2${}_1^{+}$ excited states of ${}^{150}$Sm are reported. The data recorded during 5.25 year with 36.6 g of the isotope ${}^{150}$Nd are used in the analysis. The signal of the 2νββ transition to the 0${}_1^{+}$ excited state is detected with a statistical significance exceeding 5σ. The half-life is measured to be T${}_{1/2}^{2\nu \beta \beta }$ (0${}_1^{+}$) = [1.11${}_{-0.14}^{+0.19}$ (stat)${}_{-0.15}^{+0.17}$ (syst)] × 10${}^{20}$ year, which is the most precise value that has been measured to date. 90% confidence-level limits are set for the other decay modes. For the 2νββ decay to the 2${}_1^{+}$ level the limit is T${}_{1/2}^{2\nu \beta \beta }$ (2${}_1^{+}$) > 2.42 × 10${}^{20}$ year. The limits on the 0νββ decay to the 0${}_1^{+}$ and 2${}_1^{+}$ levels of ${}^{150}$Sm are significantly improved to T${}_{1/2}^{0\nu \beta \beta }$ (0${}_1^{+}$) > 1.36 × 10${}^{22}$ year and T${}_{1/2}^{0\nu \beta \beta }$ (2${}_1^{+}$) > 1.26 × 10${}^{22}$ year.