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 $161.5pm0.3text{(stat)}pm0.3text{(syst)}$,keV from the direct $M1$ transition. Excitation energies of the $1^{-}_{2}$ and $1^{-}_{3}$ states were measured to be $2832pm3pm4$,keV and $6050pm8pm7$,keV, respectively. The obtained level energies provide definitive references for the reaction spectroscopy of $Lambda$ hypernuclei.