Four-body structure of ${}_{\Lambda }^7$Li and $\Lambda N$ spin-dependent interaction

Two spin-doublet states in ${}_{\Lambda }^7$Li are studied on the basis of the $\alpha +\Lambda +n+p$ four-body model. We employ the two-body interactions that reproduce the observed properties of any subsystems composed of $\alpha N,\alpha \Lambda$, $\alpha \mathit{NN}$, and $\alpha \Lambda N$. Furthermore, the $\Lambda N$ interaction is adjusted so as to reproduce the $0^{+}\text{−}{1}^{+}$ splitting of in ${}_{\Lambda }^4$H. The calculated energy splittings of $3/2^{+}\text{−}1/2^{+}$ and $7/2^{+}\text{−}5/2^{+}$ states in ${}_{\Lambda }^7$Li are 0.69 and 0.46 MeV, which are in good agreement with the recent observed data. The spin-dependent components of the $\Lambda N$ interaction are discussed.

Figure 1

Jacobian coordinates for all the rearrangement channels ($c=1~9$) of the $\alpha +\Lambda +n+p$ four-body model. Two nucleons are to be antisymmetrized.

Figure 2

Calculated energy levels of ${}_{\Lambda }^7$Li on the basis of $\alpha +\Lambda +n+p$ model. The energies are measured from the $\alpha +\Lambda +n+p$ threshold. The observed energy splittings of $3/2^{+}\text{−}1/2^{+}$ and $7/2^{+}\text{−}5/2^{+}$ are 0.69 and 0.47 MeV, respectively.