Low density expansion and isospin dependence of nuclear energy functional: comparison between relativistic and Skyrme models

16 pages,6 figures,5 tablesInternational audienceIn the present work we take the non relativistic limit of relativistic models and compare the obtained functionals with the usual Skyrme parametrization. Relativistic models with both constant couplings and with density dependent couplings are considered. While some models present very good results already at the lowest order in the density, models with non-linear terms only reproduce the energy functional if higher order terms are taken into account in the expansion