Relativistic and nonrelativistic calculations of the isoscalar monopole and dipole states

PTHThe study of the isoscalar giant monopole resonance (ISGMR) should allow extracting a value for the nuclear incompressibility coefficient K-infinity. In this contribution, we review the most recent attempts along this line. While the nonrelativistic (Skyrme, Gogny) models predict K-infinity to be around 220-235 MeV, the values obtained from the relativistic calculations are significantly larger (250-270 MeV). We argue that the most plausible reason for this discrepancy lies in the different behavior of the symmetry energy in the two classes of models. We also discuss the role of the isoscalar giant dipole resonance (ISGDR). We Conclude that a number of experimental ambiguities still prevent us from deducing K-infinity from the ISGDR with a comparable accuracy as from the ISGMR