Abstract
The explicit form of the next-to-next-to-leading order (N2LO) of the Skyrme effective pseudopotential compatible with all required symmetries and especially with gauge invariance is presented in a Cartesian basis. It is shown in particular that for such a pseudopotential there is no spin–orbit contribution and that the D-wave term suggested in the original Skyrme formulation does not satisfy the invariance properties. The six new N2LO terms contribute to both the equation of state and the Landau parameters. These contributions to symmetric nuclear matter are given explicitly and discussed.Communicated by Jacek Dobaczewski
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