Incompressibility of neutron-rich matter

The saturation properties of neutron-rich matter are investigated in a relativistic mean-field formalism using two accurately calibrated models: NL3 and FSUGold. The saturation properties---density, binding energy per nucleon, and incompressibility coefficient---are calculated as a function of the neutron-proton asymmetry $\ensuremath{\alpha}\ensuremath{\equiv}(N\ensuremath{-}Z)/A$ to all orders in $\ensuremath{\alpha}$. Good agreement (at the 10% level or better) is found between these numerical calculations and analytic expansions that are given in terms of a handful of bulk parameters determined at saturation density. Using insights developed from the analytic approach and a general expression for the incompressibility coefficient of infinite neutron-rich matter, i.e., ${K}_{0}(\ensuremath{\alpha})={K}_{0}+{K}_{\ensuremath{\tau}}{\ensuremath{\alpha}}^{2}+\dots{}$, we construct a hybrid model with values for ${K}_{0}$ and ${K}_{\ensuremath{\tau}}$ as suggested by recent experimental findings. Whereas the hybrid model provides a better description of the measured distribution of isoscalar monopole strength in the Sn isotopes relative to both NL3 and FSUGold, it significantly underestimates the distribution of strength in $^{208}\mathrm{Pb}$. Thus, we conclude that the incompressibility coefficient of neutron-rich matter remains an important open problem.

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