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 $K=\left(248\pm 8\right)\text{MeV}$. 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 $R_n-R_p\lesssim 0.22\text{fm}$. The impact of this result on the enhanced cooling of neutron stars is briefly addressed.

Figure 1

Distribution of isoscalar-monopole strength in ${}^{90}\mathrm{Zr}$ at a reference momentum transfer of $q=45.5\text{MeV}$. The response includes a small artificial width of $0.5\text{MeV}$.

Figure 2

Distribution of isoscalar-monopole strength in ${}^{208}\mathrm{Pb}$ at a reference momentum transfer of $q=45.5\text{MeV}$. The response includes a small artificial width of $0.5\text{MeV}$.

Figure 3

Distribution of isovector-dipole strength in ${}^{208}\mathrm{Pb}$ at a reference momentum transfer of $q=45.5\text{MeV}$. The response includes a small artificial width of $0.5\text{MeV}$.

Figure 4

Comparison between theoretical and experimental ISGMR centroid and IVGDR peak energies for ${}^{208}\mathrm{Pb}$. Quantities in parentheses represent the predictions for the neutron skin of ${}^{208}\mathrm{Pb}$ in the various models discussed in the text.