Isotopic Dependence of Giant Resonances in the Even-A ^112-124SN Isotopes and the Asymmetry Term in Nuclear Incompressibility

We have investigated the isoscalar giant resonances in the even-A Sn isotopes (A=112--124) using inelastic scattering of 400-MeV $alpha$-particles at extremely forward angles, including 0$^circ$, at the Research Center for Nuclear Physics (RCNP), Osaka University, Japan. Because of the unique optical properties of the Grand Raiden magnetic spectrometer, it was possible to obtain inelastic scattering spectra free of all instrumental background. We are able to extract strength distributions for various multipoles with multipole decomposition analysis. Essentially all of expected isoscalar giant monopole resonance (ISGMR), isoscalar giant dipole resonance (ISGDR), isoscalar giant quadrupole resonance (ISGQR) and high energy octupule resonance (HEOR) strengths were identified in these nuclei. Although the ISGMR has been identified previously in some of the Sn isotopes in measurements with inelastic $alpha$-scattering, this is the first time that it has been investigated in a large number of isotopes simultaneously. We find that the ISGMR energies in the Sn isotopes are significantly lower than the values predicted in recent theoretical calculations even though the interactions used in these calculations reproduce the GMR energies in the ``standard' nuclei, $^{208}$Pb and $^{90}$Zr, very well. Further, the asymmetry-term, K$_ au$ , has been determined to be -550 $pm$ 100 MeV from these measurements.