Ξ hypernuclear states predicted by next-to-leading-order chiral baryon–baryon interactions

Abstract The $\Xi$ single-particle potential obtained in nuclear matter with next-to-leading-order baryon–baryon interactions in chiral effective field theory is applied to finite nuclei by an improved local-density approximation method. As a premise, phase shifts of $\Xi N$ elastic scattering and the results of Faddeev calculations for the $\Xi NN$ bound state problem are presented to show the properties of the $\Xi N$ interactions in the present parametrization. First, the $\Xi$ states in $^{14}$N are revisited because of recent experimental progress, including discussion on the $\Xi N$ spin–orbit interaction that is relevant to the location of the $p$-state. Then the $\Xi$ levels in $^{56}$Fe are calculated. In particular, the level shift which is expected to be measured experimentally in the near future is predicted. The smallness of the imaginary part of the $\Xi$ single-particle potential is explicitly demonstrated.