Compression modes in nuclei: microscopic models with Skyrme interactions

The isoscalar giant monopole resonances (ISGMR) and giant dipole resonances (ISGDR) in medium-heavy nuclei are investigated in the framework of HF+RPA and HF-BCS+QRPA with Skyrme effective interactions. It is found that pairing has little effect on these modes. It is also found that the coupling of the RPA states to 2p-2h configurations results in about (or less than) 1 MeV shifts of the resonance energies and at the same time gives the correct total widths. For the ISGMR, comparison with recent data leads to a value of nuclear matter compression modulus close to 215 MeV. However, a discrepancy between calculated and measured energies of the ISGDR in $^{208}$Pb is found and remains an open problem.