Impact of Effective Nucleon Mass and Multineutron States on the Equation of State for Core-Collapse Supernovae
In this study, we investigate the impact of effective nucleon mass and the existence of the dineutron $(\mathrm{^{2}n})$ and the tetraneutron $(\mathrm{^{4}n})$ on the thermodynamic properties and nuclear compositions by constructing new equations of state. Our results indicate that the model with a larger effective nucleon mass slightly alters the nuclear composition in neutron-rich environments primarily due to differences in the symmetry energy: the mass fractions of unbound neutrons, protons, and heavy nuclei increase. The impact on the thermodynamic properties is negligible, except for the chemical potentials. On the other hand, multineutron states become prominent at high densities in neutron-rich environments, leading to a substantial reduction in the unbound neutron fraction. This depletion lowers the chemical potential of unbound neutrons, which in turn reduces the abundance of neutron-rich nuclei. Consequently, the number of unbound protons increases, leading to a corresponding rise in proton chemical potential. These shifts in chemical potentials promote the formation of heavy nuclei with larger mass and atomic numbers. Ultimately, this compositional shift results in a lower free energy, primarily driven by the emergence of these heavy nuclei.