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We discuss some infinite matter properties of two finite-range interactionswidely used for nuclear structure calculations, namely Gogny and M3Yinteractions. We show that some useful informations can be deduced for thecentral, tensor and spin-orbit terms from the spin-isospin channels and thepartial wave decomposition of the symmetric nuclear matter equation of state.We show in particular that the central part of the Gogny interaction shouldbenefit from the introduction of a third Gaussian and the tensor parameters ofboth interactions can be deduced from special combinations of partial waves. Wealso discuss the fact that the spin-orbit of the M3Y interaction is notcompatible with local gauge invariance. Finally, we show that the zero-rangelimit of both families of interactions coincides with the specific form of thezero-range N3LO Skyrme interaction and we emphasize from this analogy thebenefits of N3LO.

Infinite matter properties and zero-range limit of nonrelativistic finite-range interactions