Mic-Mac model based on the Wigner-Kirkwood method

About a decade ago we proposed a new Microscopic-Macroscopic (Mic-Mac) model where the semiclassical Wigner-Kirkwood expansion of the energy up to fourth-order in ħ is used to compute the shell corrections in a deformed Woods-Saxon potential instead of the usual Strutinsky averaging scheme [1,2]. For a set of 551 even-even nuclei computed with this new model, we found a rms deviation of 610 keV from the experimental masses, similar to the value obtained using the well-known Finite Range Droplet Model and the Lublin-Strasbourg Drop Model for the same set of nuclei. In a next step, we compute the ground-state properties of these 551 nuclei with the same method but using the mean-field provided by the Gogny forces within an Extended Thomas-Fermi approximation. We find that this Mic-Mac model using the Gogny D1S (D1M) force gives a fairly good description of the ground-state energies with a rms deviation of 834 keV (819 keV). This implies that Mic-Mac models based on effective two-body forces, for example Gogny D1S and D1M interactions, perform practically as well as the most efficient Mic-Mac models regarding ground-state properties.