The meaningful correlations between the zero-sound modes and the stiffness of the nuclear equation of state (EOS) are uncovered in nuclear matter with the relativistic mean-field theory. It is demonstrated that the high-density zero-sound modes merely exist in models with the stiff EOS. While the stiff EOS can be softened by including $\omega$-meson self-interactions (the ${\omega }^4$ term), the weakened coupling of the $\omega$-meson self-interactions reignites the zero sound at high density. These results suggest that the high-density zero-sound modes can be used to probe the stiffness of the EOS at supra-normal densities. The implications and effects of zero sounds are also discussed in heavy ion collisions and neutron stars.

• Received 12 December 2022
• Revised 28 July 2023
• Accepted 20 September 2023

DOI:https://doi.org/10.1103/PhysRevC.108.044312