Impact of ground-state properties and collective excitations on the Skyrme ansatz: A Bayesian study

State-of-the-art models based on nuclear density functional theory are successful in the description of nuclei throughout the whole nuclear chart. Among them, some differences arise regarding their accuracy. For a given nuclear model, this depends on the procedure adopted to determine the parameters, and, at the same time, new experimental findings constantly challenge theory. In the present work, we present a Bayesian inference study aimed at assessing the performance of the Skyrme energy density functionals. For the sake of simplicity and clarity, we restrict our study to spherical, double-magic nuclei, giving equal emphasis to ground-state and dynamical properties. Our basic constraints are (i) masses and charge radii, which are known to be very sensitive to the saturation energy and density; (ii) spin-orbit splittings, which are associated with the spin-orbit parameter(s); (iii) the electric dipole polarizability and parity-violating asymmetry, which are associated with the density dependence of the symmetry energy; (iv) the excitation energy of the isoscalar giant monopole resonance, to constrain the nuclear matter incompressibility; (v) the energy-weighted sum rule of the isovector giant dipole resonance, to account for the isovector effective mass; and (vi) the excitation energy of the isoscalar quadrupole resonance, which is related to the isoscalar effective mass. We are then able to test the Skyrme ansatz in a statistically meaningful way, by determining the posterior distributions of the parameters. In particular, we have found probability distributions in line with published results, with the only exceptions of the symmetry energy at saturation $J$ and its slope $L$, whose distributions favor lower values than commonly reported. Using our method, we have also been able to discuss the correlations among parameters and observables. Finally, we discuss a few possible future developments.