Tensor coupling effects on spin symmetry in anti-Lambda spectrum of hypernuclei

The effects of $\bar\Lambda\bar\Lambda\omega$-tensor coupling on the spin symmetry of $\bar{\Lambda}$ spectra in $\bar{\Lambda}$-nucleus systems have been studied with the relativistic mean-field theory. Taking $^{12}$C+$\bar{\Lambda}$ as an example, it is found that the tensor coupling enlarges the spin-orbit splittings of $\bar\Lambda$ by an order of magnitude although its effects on the wave functions of $\bar{\Lambda}$ are negligible. Similar conclusions has been observed in $\bar{\Lambda}$-nucleus of different mass regions, including $^{16}$O+$\bar{\Lambda}$, $^{40}$Ca+$\bar{\Lambda}$ and $^{208}$Pb+$\bar{\Lambda}$. It indicates that the spin symmetry in anti-lambda-nucleus systems is still good irrespective of the tensor coupling.