We discuss the contributions to the equation of state for the $\text{N}\ell \text{LO}$ Skyrme pseudopotential $(\ell =2,3)$. We show that by adding fourth- and sixth-order gradient terms, it is possible to fairly reproduce the spin/isospin decomposition of an equation of state obtained from ab initio methods. Moreover, by inspecting the partial-wave decomposition of the equation of state, we show for the first time a possible way to add explicit constraints on the sign of the tensor terms of the Skyrme interaction.

• Received 5 March 2015

DOI:https://doi.org/10.1103/PhysRevC.91.064303