Instabilities of infinite matter with effective Skyrme-type interactions

The stability of the equation of state predicted by Skyrme-type interactions is examined. We consider simultaneously symmetric nuclear matter and pure neutron matter. The stability is defined by the inequalities that the Landau parameters must satisfy simultaneously. A systematic study is carried out to define interaction parameter domains where the inequalities are fulfilled. It is found that there is always a critical density $\rho_{cr}$ beyond which the system becomes unstable. The results indicate in which parameter regions one can find effective forces to describe correctly finite nuclei and give at the same time a stable equation of state up to densities of 3-4 times the saturation density of symmetric nuclear matter.