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.
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