Determination of the parameters of a Skyrme type effective interaction using the simulated annealing approach

We implement for the first time the simulated annealing method to the problem of searching for the global minimum in the hypersurface of the χ² function, which depends on the values of the parameters of a Skyrme-type effective nucleon-nucleon interaction. We undertake a realistic case of fitting the values of the Skyrme parameters to an extensive set of experimental data on the ground-state properties of many nuclei, ranging from normal to exotic ones. The set of experimental data used in our fitting procedure includes the radii for the valence 1d_5/2 and 1f_7/2 neutron orbits in the ¹⁷O and ⁴¹Ca nuclei, respectively, and the breathing-mode energies for several nuclei, in addition to the typically used data on binding energy, charge radii, and spin-orbit splitting. We also include in the fit the critical density ρ_cr and further constrain the values of the Skyrme parameters by requiring that (i) the quantity P=3ρ(dS/dρ), directly related to the slope of the symmetry energy S, must be positive for densities up to 3ρ₀; (ii) the enhancement factor κ, associated with the isovector giant dipole resonance, should lie in the range of 0.1–0.5; and (iii) the Landau parameter G₀^' is positive at ρ=ρ₀. We provide simple but consistent schemes to account for the center-of-mass corrections to the binding energy and charge radii.