Do we understand the incompressibility of neutron-rich matter?

The ``breathing mode'' of neutron-rich nuclei is our window into the incompressibility of neutron-rich matter. After much confusion on the interpretation of the experimental data, consistency was finally reached between different models that predicted both the distribution of isoscalar monopole strength in finite nuclei and the compression modulus of infinite matter. However, a very recent experiment on the Tin isotopes at the Research Center for Nuclear Physics(RCNP) in Japan has again muddled the waters. Self-consistent models that were successful in reproducing the energy of the giant monopole resonance (GMR) in nuclei with various nucleon asymmetries (such as 90Zr, 144Sm, and 208Pb) overestimate the GMR energies in the Tin isotopes. As important, the discrepancy between theory and experiment appears to grow with neutron excess. This is particularly problematic as models artificially tuned to reproduce the rapid softening of the GMR in the Tin isotopes become inconsistent with the behavior of dilute neutron matter. Thus, we regard the question of ``why is Tin so soft?'' as an important open problem in nuclear structure.