Correlating the giant-monopole resonance to the nuclear-matter incompressibility

Differences in the density dependence of the symmetry energy predicted by nonrelativistic and relativistic models are suggested, at least in part, as the culprit for the discrepancy in the values of the compression modulus of symmetric nuclear matter extracted from the energy of the giant monopole resonance in ²⁰⁸Pb. ``Best-fit'' relativistic models, with stiffer symmetry energies than Skyrme interactions, consistently predict higher compression moduli than nonrelativistic approaches. Relativistic models with compression moduli in the physically acceptable range of K=200--300MeV are used to compute the distribution of isoscalar monopole strength in ²⁰⁸Pb. When the symmetry energy is artificially softened in one of these models, in an attempt to simulate the symmetry energy of Skyrme interactions, a lower value for the compression modulus is indeed obtained. It is concluded that the proposed measurement of the neutron skin in ²⁰⁸Pb, aimed at constraining the density dependence of the symmetry energy and recently correlated to the structure of neutron stars, will also become instrumental in the determination of the compression modulus of nuclear matter.