content_image/356498.jpg content_image/356499.jpg
<img src='content_image/356498.jpg'>

<img src='content_image/356499.jpg'>

comparison with the RMF results (see Fig. 2 in Ref. [15]), the DDRHF results have the following characteristics: 1) the spin-orbit splittings are smaller; 2) the spin-orbit splittings fluctuate with E$_{av}$ , in contrast with the monotonous decreasing in the RMF case, when approaching the continuum limit; 3) in RMF the spin-down state ( j = ˜ l − 1 / 2) is always lower than its spin-up partner ( j = ˜ l + 1 / 2), while in DDRHF this occurs only for the p orbits and states near the continuum limit. 

In order to understand the origin of the spin symmetry in DDRHF and the relative positions of the spin-up state and its spin-down partner, the effective potentials V in Eq. 

