PT Journal AU Davesne, D Pastore, A Navarro, J TI Skyrme effective pseudopotential up to the next-to-next-to-leading order SO Journal of Physics G JI J. Phys. G PY 2013 BP 095104 EP 8pp VL 40 IS 9 DI 10.1088/0954-3899/40/9/095104 LA English AB The explicit form of the next-to-next-to-leading order ((NLO)-L-2) 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 (NLO)-L-2 terms contribute to both the equation of state and the Landau parameters. These contributions to symmetric nuclear matter are given explicitly and discussed. ER