CoherentΛ−ΣCoupling ins-Shell Hypernuclei

It is found that the suppression due to two-body $\Lambda N-\Sigma N$ coupling solves the overbinding problem in ${}_{\Lambda }^5\mathrm{He}$ but it, in turn, causes a severe underbinding in the four-body systems. The shortage of this binding is overcome by introducing explicitly the $\Lambda -\Sigma$ coupling which is equivalent to the $\Lambda \mathrm{NN}$ three-body force. This three-body force becomes strong in the $0^{+}$ states of ${}_{\Lambda }^4\mathrm{H}$ and ${}_{\Lambda }^4\mathrm{He}$ according to the coherently added enhancement. The $0^{+}-1^{+}$ splitting in ${}_{\Lambda }^4\mathrm{H}$ and ${}_{\Lambda }^4\mathrm{He}$ is found partly due to the $\Lambda N$ spin-spin interaction and partly due to the $\Lambda -\Sigma$ coupling in the recent Nijmegen soft-core potential.