Gogny force with a finite-range density dependence

In the present work, we have investigated an extension of the effective nucleon-nucleon Gogny interaction in which the zero-range density-dependent term has been replaced with a finite-range term. The parameters have been adjusted on both nuclear-matter properties and a few observables of stable nuclei. The traditional and unified fitting procedure of the Gogny force used in Bruy\`eres-le-Ch\^atel ensures common basic properties between the extended analytical form of the Gogny interaction, called $D2$, and the original one. In particular, symmetric infinite nuclear-matter and neutron-matter properties as well as pairing correlations have been investigated. A few static properties obtained in finite nuclei using the Hartree-Fock-Bogoliubov approach and the $D2$ parametrization of the Gogny interaction are analyzed and compared to the results obtained with $D1$-type parametrizations and experiment when it is possible. The $D2$ parametrization makes it possible to reproduce nuclear structure properties with improved accuracy.