Fitting Skyrme functionals using linear response theoryFitting Skyrme functionals using linear response theory

It has recently been shown that the linear response theory in symmetric nuclear matter can be used as a tool for detecting finite-size instabilities for different Skyrme functionals. In particular, it has been shown that there is a correlation between the density at which instabilities occur in infinite matter and the instabilities in finite nuclei. In this paper, we present a new fitting protocol that uses this correlation to add a new additional constraint in symmetric infinite nuclear matter in order to ensure the stability of finite nuclei against matter fluctuation in all spin and isospin channels. As an application, we give the parameter set for a new Skyrme functional which includes central and spin-orbit parts and which is free from instabilities by construction.