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 ⁹⁰Zr and ²⁰⁸Pb, and the isovector-dipole strength in ²⁰⁸Pb using a continuum random-phase-approximation approach. It is shown that the distribution of isoscalar-monopole strength in ²⁰⁸Pb---but not in ⁹⁰Zr---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 ²⁰⁸Pb. Thus, one relies on ⁹⁰Zr, 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±8)0.3em0exMeV. In turn, the sensitivity of the ISGMR in ²⁰⁸Pb to the density dependence of the symmetry energy is used to constrain its neutron skin to the range Rₙ-Rₚ0.220.3em0exfm. The impact of this result on the enhanced cooling of neutron stars is briefly addressed.