Abstract
We perform a coupled-channels study of the low-lying states in $^{13,15,17,19}_{~~~~~~~~~~~~~~~~~~~~~\Lambda}$C with a covariant energy density functional based microscopic particle-core coupling model. The energy differences of $1/2^-$ and $3/2^-$ states in $^{13}_\Lambda$C and $^{15}_\Lambda$C are predicted to be 0.25 MeV and 0.34 MeV, respectively. We find that configuration mixings in the $1/2^-$ and $3/2^-$ states of $^{15}_\Lambda$C are the weakest among those of $^{13,15,17,19}_{~~~~~~~~~~~~~~~~~~~~~\Lambda}$C. It indicates that $^{15}_\Lambda$C provides the best candidate among the carbon hypernuclei to study the spin-orbit splitting of $p_\Lambda$ hyperon state.
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