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

Background: The equation of state (EOS) $E(\ensuremath{\rho},\ensuremath{\delta})$ neutron-rich nucleonic matter at density $\ensuremath{\rho}$ and isospin asymmetry $\ensuremath{\delta}$ can be approximated as the sum symmetric nuclear (SNM) EOS ${E}_{0}(\ensuremath{\rho})$ a power series in ${\ensuremath{\delta}}^{2}$ with coefficient ${E}_{\text{sym}}(\ensuremath{\rho})$ its first term so-called symmetry energy. Great effort has been devoted to studying characteristics both SNM energy using various experiments theories over last few decades. While much progress made constraining parameters characterizing around saturation ${\ensuremath{\rho}}_{0}$ SNM, such incompressibility ${K}_{0}$ well magnitude $S$ slope $L$ symmetry, high-density behaviors ${E}_{\text{sym}}(\ensuremath{\rho})$, skewness ${J}_{0}$ kurtosis ${I}_{0}$ curvature ${K}_{\text{sym}}$ ${J}_{\text{sym}}$ are still poorly known. Moreover, most attention put on separately if completely independent.Purpose: Because pure neutron (PNM) is all coefficients expanding ${\ensuremath{\delta}}^{2}$, unbound nature PNM requires intrinsic correlations between those independent any many-body theory. We investigate these their applications better known behavior energy.Method: derive an expression for ${\ensuremath{\rho}}_{\text{sat}}(\ensuremath{\delta})$ up order ${\ensuremath{\delta}}^{6}$ terms parameters. Setting ${\ensuremath{\rho}}_{\text{sat}}(\ensuremath{\delta})=0$ required by leads rule then analyze this different orders find approximate expressions relatively determined ${\ensuremath{\rho}}_{0}$.Results: Several novel connecting found. In particular, lowest-order approximations, bulk parts $L$, ${K}_{\text{sym}}$, found $L\ensuremath{\approx}{K}_{0}/3, {K}_{\text{sym}}\ensuremath{\approx}L{J}_{0}/2{K}_{0}$, ${J}_{\text{sym}}\ensuremath{\approx}{I}_{0}L/3{K}_{0}$, respectively. High-order corrections simple relations written small ratios high-order resulting among some reproduce very nicely predicted microscopic phenomenological models constrained available data terrestrial astrophysical observations literature.Conclusion: fundamental universal. These provide model-independent tool not only consistency checks but also investigating properties smaller uncertainties.