Fitting N³LO pseudopotentials through central plus tensor Landau parameters

Landau parameters determined from phenomenological finite-range interactions are used to get an estimation of N$^3$LO pseudopotentials parameters. The parameter sets obtained in this way are shown to lead to consistent results concerning saturation properties. The uniqueness of this procedure is discussed, and an estimate of the error induced by the truncation at N$^3$LO is given.