Spin-orbit energy density

A complete isospin dependence of the spin-orbit term [15] has already been implemented in several standard Skyrme forces. Within such a generalized parametrization, the isoscalar and isovector coupling constants, which define the spin-orbit term, see Eq. (I-12), read while the traditional parametrization requires that $W'_0 \equiv W_0$. Here, $W_0$ is the strength of the two-body spin-orbit part of the Skyrme force [16,17]. The corresponding parameters used in Ref. [15] are $b_4$= ${\textstyle{\frac{1}{2}}}W_0$ and $b'_4$= ${\textstyle{\frac{1}{2}}}W'_0$.

The code HFODD uses the energy density coupling constants, and not the parameters of the Skyrme force, so generalization (17) has always been available through appropriate scaling of the coupling constants, see Sec. II-3.2. In the new version (v2.07f), the use of the above generalization was facilitated by introducing explicit input data parameters that allow to directly handle the strengths $W'_0$ and $W_0$.