Determination of the parameters of a Skyrme type effective interaction using the simulated annealing approach
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We implement for the first time the simulated annealing method to the problem of searching for the global minimum in the hypersurface of the 2 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 1d5/2 and 1f7/2 neutron orbits in the O17 and Ca41 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 cr and further constrain the values of the Skyrme parameters by requiring that (i) the quantity P=3(dS/d), directly related to the slope of the symmetry energy S, must be positive for densities up to 30; (ii) the enhancement factor , 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 =0. We provide simple but consistent schemes to account for the center-of-mass corrections to the binding energy and charge radii. 2005 The American Physical Society.