Precise determination of $^{12}_{\Lambda}$C level structure by $\gamma$-ray spectroscopy

Level structure of the $^{12}_{\Lambda}$C hypernucleus was precisely determined by means of $\gamma$-ray spectroscopy. We identified four $\gamma$-ray transitions via the $^{12}$C$(\pi^{+},K^{+}\gamma)$ reaction using a germanium detector array, Hyperball2. The spacing of the ground-state doublet $(2^{-}_{1},1^{-}_{1})$ was measured to be $161.5\pm0.3\text{(stat)}\pm0.3\text{(syst)}$\,keV from the direct $M1$ transition. Excitation energies of the $1^{-}_{2}$ and $1^{-}_{3}$ states were measured to be $2832\pm3\pm4$\,keV and $6050\pm8\pm7$\,keV, respectively. The obtained level energies provide definitive references for the reaction spectroscopy of $\Lambda$ hypernuclei.