[en] Deformed and spherical even–even nuclei are studied using a finite-range simple effective interaction within the Hartree–Fock–Bogoliubov mean-field approach. Different parameter sets of the interaction, corresponding to different incompressibility, are constructed by varying the exponent γ of the density in the traditional density-dependent term. Ten of the 12 parameters of these interactions are determined from properties of asymmetric nuclear matter and spin-polarized pure neutron matter. The two remaining parameters are fitted to reproduce the experimental binding energies known in 620 even–even nuclei using several variants of the rotational energy correction. The rms deviations for the binding energy depend on the value of γ and the way the rotational energy correction is treated but they can be as low as 1.56 MeV, a value competitive with other renowned effective interactions of Skyrme and Gogny type. Charge radii are compared to the experimental values of 313 even–even nuclei and the rms deviation is again comparable and even superior to the one of popular Skyrme and Gogny forces. Emphasis is given to the deformation properties predicted with these interactions by analyzing the potential energy surfaces for several well deformed nuclei and the fission barriers of some nuclei. Comparison of the results with the experimental information, where available, as well as with the results of the Gogny D1S force, shows satisfactory agreement. (paper)