Recently, it has been recently shown that the linear response theory in symmetric nuclear matter can be used as a tool to detect finite size instabilities for different Skyrme functionals. In particular it has been shown that there is a correlation b
etween the density at which instabilities occur in infinite matter and the instabilities in finite nuclei. In this article we present a new fitting protocol that uses this correlation to add 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 parameters set for a new Skyrme functional which includes central and spin-orbit parts and which is free from instabilities by construction.
Nuclear effective interactions are often modelled by simple analytical expressions such as the Skyrme zero-range force. This effective interaction depends on a limited number of parameters that are usually fitted using experimental data obtained from
doubly magic nuclei. It was recently shown that many Skyrme functionals lead to the appearance of instabilities, in particular when symmetries are broken, for example unphysical polarization of odd-even or rotating nuclei. In this article, we show how the formalism of the linear response in infinite nuclear matter can be used to predict and avoid the regions of parameters that are responsible for these unphysical instabilities.
