BREATHING MODE IN FINITE NUCLEI AND THE EQUATION-OF-STATE OF NUCLEAR-MATTER

Procedures are reviewed to deduce the incompressibility modulus of infinite, symmetric, cold nuclear matter at saturation density, K-x, from the energies of IsoscaIar Giant Monopole Resonances, ISGMR, in finite nuclei. Neither the quality of the data nor the state-of-the-art theory permit to determine the K-t value to better than within a factor of 1.5-1.7. This is compared with the corresponding ranges of K-t values stemming from other nuclear and astrophysical observations, such as those for nuclear masses and radii, nucleus-nucleus collisions, supernovae explosions and neutron stars. Uncertainties associated with these values are generally even much larger than in the case of those deduced from the ISGMR data. This implies serious uncertainty in prescribing the Equation-Of-State for nuclear matter and thus also in predicting properties of e.g. dense stellar objects. A better K-t value for nuclear matter under ''normal'' conditions is urgently needed. Ways to improve the quality of ISGMR data necessary for this purpose are discussed. Of particular importance are high precision measurements for closed shell nuclei as well as new data for nuclei away of the stability line. The experimental progress should be parallelled by a theoretical effort in order to minimize the model dependence of the K-t value deduced from the ISGMR data.