Intrinsic correlations among characteristics of neutron-rich matter imposed by the unbound nature of pure neutron matter

The unbound nature of pure neutron matter (PNM) requires intrinsic correlations between the symmetric nuclear matter (SNM) EOS parameters (incompressibility $K_0$, skewness $J_0$ and kurtosis $I_0$) and those (slope $L$, curvature $K_{\rm{sym}}$ and skewness $J_{\rm{sym}}$) characterizing the symmetry energy independent of any nuclear many-body theory. We investigate these intrinsic correlations and their applications in better constraining the poorly known high-density behavior of nuclear symmetry energy. Several novel correlations connecting the characteristics of SNM EOS with those of nuclear symmetry energy are found. In particular, at the lowest-order of approximations, the bulk parts of the slope $L$, curvature $K_{\rm{sym}}$ and skewness $J_{\rm{sym}}$ of the symmetry energy are found to be $L\approx K_0/3, K_{\rm{sym}}\approx LJ_0/2K_0$ and $J_{\rm{sym}}\approx I_0L/3K_0$, respectively. High-order corrections to these simple relations can be written in terms of the small ratios of high-order EOS parameters. The resulting intrinsic correlations among some of the EOS parameters reproduce very nicely their relations predicted by various microscopic nuclear many-body theories and phenomenological models constrained by available data of terrestrial experiments and astrophysical observations in the literature. The unbound nature of PNM is fundamental and the required intrinsic correlations among the EOS parameters characterizing both the SNM EOS and symmetry energy are universal. These intrinsic correlations provide a novel and model-independent tool not only for consistency checks but also for investigating the poorly known high-density properties of neutron-rich matter by using those with smaller uncertainties.