  A unified description of finite nuclei and equation of state of neutron stars
present a major challenge as well as opportunities for understandings of
nuclear interactions.Inspired by the Lee-Huang-Yang formula of hard-sphere
gases, we developed effective nuclear interactions with an additional
high-order density dependent term.The original Skyrme force SLy4 is widely used
in studies of neutron stars but is not satisfied for global descriptions of
finite nuclei. The refitted SLy4${'}$ force can improve descriptions of finite
nuclei but slightly reduces the radius of neutron star of 1.4 solar mass.We
found that the extended SLy4 force with a higher-order density dependence can
properly describe properties of both finite nuclei and GW170817 binary neutron
stars, including the mass-radius relation and the tidal deformability. This
demonstrated the essential role of high-order density dependence at ultrahigh
densities. Our work provides a unified and predictive model for neutron stars,
as well as new insights for the future development of effective interactions.
