Impact of choices for center-of-mass correction energy on the surface energy of Skyrme energy density functionals

In the framework of nuclear energy density functional (EDF) methods, many nuclear phenomena can be related to the deformation of intrinsic states. Their accurate modeling relies on the correct description of the change of nuclear binding energy with deformation. The two most important contributions to the deformation energy have their origin in shell effects and the surface energy coefficient of nuclear matter. In a first step, we build nine series of parametrizations with a systematically varied surface-energy coefficient a_surf for three frequently-used options for the CM correction (none, one-body term only, full one-body and two-body contributions) combined with three values for the isoscalar effective mass m^*_0/m (0.7, 0.8, 0.85) and analyse how well each of these parametrizations can be adjusted to the properties of spherical nuclei and infinite nuclear matter. In a second step, we performed additional fits without the constraint on surface energy, adding one ``best-fit"parametrization to each of the nine series. We then benchmark these parametrizations to the deformation properties of heavy nuclei by means of three-dimensional Hartree-Fock-Bogoliubov calculations that allow for non-axial and/or non-reflection symmetric configurations. We perform a detailed correlation analysis between surface and volume properties of nuclear matter using the nine series of parametrizations. The best fits out of each series are then benchmarked on the fission barriers of Pu240 and Hg180, as well as on the properties of deformed states at normal and superdeformation for actinides and nuclei in the neutron-deficient Hg region. (see paper for full abstract)