Unmasking the nuclear matter equation of state

Accurately calibrated (or ``best fit'') relativistic mean-field models are used to compute the distribution of isoscalar-monopole strength in $^{90}\mathrm{Zr}$ and $^{208}\mathrm{Pb}$, and the isovector-dipole strength in $^{208}\mathrm{Pb}$ using a continuum random-phase-approximation approach. It is shown that the distribution of isoscalar-monopole strength in $^{208}\mathrm{Pb}$---but not in $^{90}\mathrm{Zr}$---is sensitive to the density dependence of the symmetry energy. This sensitivity hinders the extraction of the compression modulus of symmetric nuclear matter from the isoscalar giant monopole resonance (ISGMR) in $^{208}\mathrm{Pb}$. Thus, one relies on $^{90}\mathrm{Zr}$, a nucleus with both a small neutron-proton asymmetry and a well developed ISGMR peak, to constrain the compression modulus of symmetric nuclear matter to the range $K=(248\ifmmode\pm\else\textpm\fi{}8)\phantom{\rule{0.3em}{0ex}}\text{MeV}$. In turn, the sensitivity of the ISGMR in $^{208}\mathrm{Pb}$ to the density dependence of the symmetry energy is used to constrain its neutron skin to the range ${R}_{n}\ensuremath{-}{R}_{p}\ensuremath{\lesssim}0.22\phantom{\rule{0.3em}{0ex}}\text{fm}$. The impact of this result on the enhanced cooling of neutron stars is briefly addressed.

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