# Configuration mixing in low-lying spectra of carbon hypernuclei

## TL;DR

This study uses a microscopic particle-core coupling model to analyze low-lying states in carbon hypernuclei, predicting energy differences and configuration mixings, highlighting $^{15}_ extLambda$C as ideal for studying spin-orbit splitting of the $p_ extLambda$ hyperon.

## Contribution

It introduces a covariant energy density functional based microscopic model to analyze configuration mixing and energy differences in carbon hypernuclei, emphasizing $^{15}_ extLambda$C's suitability for spin-orbit splitting studies.

## Key findings

- Predicted energy differences of 0.25 MeV and 0.34 MeV for specific states.
- Configuration mixing is weakest in $^{15}_ extLambda$C.
- $^{15}_ extLambda$C is the best candidate for studying $p_ extLambda$ spin-orbit splitting.

## 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.