Study of the C-13(Lambda) hypernucleus by the C-13(K-, pi- gamma) reaction

The ${}_{\ensuremath{\Lambda}}^{13}\mathrm{C}$ hypernucleus was studied by measuring $\ensuremath{\gamma}$ rays in coincidence with the ${}^{13}\mathrm{C}{(K}^{\ensuremath{-}},{\ensuremath{\pi}}^{\ensuremath{-}})$ reaction. $\ensuremath{\gamma}$ rays from the ${1/2}^{\ensuremath{-}}$ and ${3/2}^{\ensuremath{-}}$ states, which are the partners of the spin-orbit doublet states with a predominant configuration of ${[}^{12}{\mathrm{C}}_{\mathrm{g}.\mathrm{s}.}{(0}^{+})\ensuremath{\bigotimes}{p}_{\ensuremath{\Lambda}}],$ to the ground state were measured. The splitting of the states was found to be $\ensuremath{\Delta}{E(1/2}^{\ensuremath{-}}\ensuremath{-}{3/2}^{\ensuremath{-}})=+152\ifmmode\pm\else\textpm\fi{}54(\mathrm{stat})\ifmmode\pm\else\textpm\fi{}36(\mathrm{syst}) \mathrm{keV}.$ This value is 20--30 times smaller than that of single particle states in nuclei around this mass region. The ${j}_{\ensuremath{\Lambda}}={\mathcal{l}}_{\ensuremath{\Lambda}}\ensuremath{-}1/2[{(p}_{1/2}{)}_{\ensuremath{\Lambda}}]$ state appeared higher in energy, as in normal nuclei. The value gives new insight into the $\mathrm{YN}$ interaction. The excitation energies of the ${1/2}^{\ensuremath{-}}$ and ${3/2}^{\ensuremath{-}}$ states were obtained as $10.982\ifmmode\pm\else\textpm\fi{}0.031(\mathrm{stat})\ifmmode\pm\else\textpm\fi{}0.056(\mathrm{syst})$ and $10.830\ifmmode\pm\else\textpm\fi{}0.031(\mathrm{stat})\ifmmode\pm\else\textpm\fi{}0.056(\mathrm{syst}) \mathrm{MeV},$ respectively. We also observed $\ensuremath{\gamma}$ rays from the ${3/2}^{+}$ state, which has a ${[}^{12}\mathrm{C}{(2}^{+})\ensuremath{\bigotimes}{s}_{\ensuremath{\Lambda}}]$ configuration, to the ground state in ${}_{\ensuremath{\Lambda}}^{13}\mathrm{C}.$ The excitation energy of the ${3/2}^{+}$ state was obtained as $4.880\ifmmode\pm\else\textpm\fi{}0.010(\mathrm{stat})\ifmmode\pm\else\textpm\fi{}0.017(\mathrm{syst}) \mathrm{MeV}.$ Nuclear $\ensuremath{\gamma}$ rays with energies of 4.438 and 15.100 MeV had similar yields, which suggests that a quasifree knockout of a $\ensuremath{\Lambda}$ particle is dominant in highly excited regions.