th / 0 30 90 02 v 1 3 1 A ug 2 00 3 1 Theoretical understanding of the nuclear incompressibility : where do we stand ?

The status of the theoretical research on the compressional modes of finite nuclei and the incompressibility K∞ of nuclear matter, is reviewed. It is argued that the recent experimental data on the Isoscalar Giant Monopole Resonance (ISGMR) allow extracting the value of K∞ with an uncertainity of about ± 15 MeV. Non-relativistic (Skyrme, Gogny) and relativistic mean field models predict for K∞ values which are significantly different from one another, namely ≈ 220-235 and ≈ 250-270 MeV respectively. It is shown that the solution of this puzzle requires a better determination of the symmetry energy at, and around, saturation. The role played by the experimental data of the Isoscalar Giant Dipole Resonance (ISGDR) is also discussed.