Abstract. We present a new two-body finite-range and momentum-dependent but density-independent e ff ective interaction, which can be interpreted as a regularized zero- range force. We show that no three-body or density-dependent terms are needed for a correct description of saturation properties in infinite matter, that is, on the level of low- energy density functional, the physical three-body e ff ects can be e ffi ciently absorbed in e ff ective two-body terms. The new interaction gives a satisfying equation of state of nuclear matter and opens up extremely interesting perspectives for the mean-field and beyond-mean-field descriptions of atomic nuclei.